A 12 feet ladder leans against the side of a house. The bottom of the ladder is 9 feet from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth. We have a right triangle, where 12 is the hypotenuse. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=9&hypinput=12&pl=Solve+Missing+Side']Using our right triangle calculator[/URL], we get: side = [B]7.9[/B]

A 13 ft. ladder is leaning against a building 12 ft. up from the ground. How far is the base of the ladder from the building? This is a classic 5-12-13 pythagorean triple, where the hypotenuse is 13, and the 2 sides are 5 and 12. The building and the ground form a right triangle. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=12&hypinput=13&pl=Solve+Missing+Side']You can see the proof here[/URL]...

A 13ft ladder leans against the side of a house. The bottom of the ladder is 10ft from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth. We have a right triangle. Hypotenuse = 13, one leg = 10. We use our [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=10&hypinput=13&pl=Solve+Missing+Side']Pythagorean theorem Calculator to solve for the other leg[/URL]: s = [B]8.3066[/B]

A 5 foot ladder is leaning against a wall. If the bottom of the ladder is 3 feet from the base of the wall, how high up the wall is the top of the ladder? The answer is [B]4[/B]. Since we have a right triangle, with special ratio 3-4-5. The ladder represents the hypotenuse.

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of the two poles, what is the minimum length of cord you would need? The difference between the 70 foot and 50 foot pole is: 70 - 50 = 20 foot height difference. So we have a right triangle, with a height of 20, base of 30. We want to know the hypotenuse. Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=20&side2input=30&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator to solve for hypotenuse[/URL], we get: hypotenuse = [B]36.06 feet[/B]

A 74 inch rake is Leaning against a wall. The top of the rake hits the wall 70 inches above the ground. How far is the bottom of the rake from the base of the wall? We have a right triangle. Hypotenuse is the rake length fo 74 inches. One of the legs is 70. We [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=70&hypinput=74&pl=Solve+Missing+Side']use our right triangle calculator to solve for the other leg[/URL]: [B]24 inches[/B]

A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the tree. How tall is the tree? So we have a [U]right triangle[/U]. Hypotenuse is 15. Base is 12. We want the length of the leg. The formula for a right triangle relation of sides is a^2 + b^2 = c^2 where c is the hypotenuse and a, b are the sides Rearranging this equation to isolate a, we get a^2 = c^2 - b^2 Taking the square root of both sides, we get a = sqrt(c^2 - b^2) a = sqrt(15^2 - 12^2) a = sqrt(225 - 144) a = sqrt(81) a = [B]9 meters[/B]

A computer screen has a diagonal dimension of 19 inches and a width of 15 inches. Approximately what is the height of the screen? We have a right triangle, with hypotenuse of 19, and width of 15. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=15&hypinput=19&pl=Solve+Missing+Side']Using our right triangle calculator, we get [/URL][B]height = 11.662[/B]

A helicopter rose vertically 300 m and then flew west 400 m how far was the helicopter from it’s starting point? The distance forms a right triangle. We want the distance of the hypotenuse. Using our [URL='http://www.mathcelebrity.com/pythag.php?side1input=300&side2input=400&hypinput=&pl=Solve+Missing+Side']right triangle calculator[/URL], we get a distance of [B]500[/B]. We also could use a shortcut on this problem. If you divide 300 and 400 by 100, you get 3 and 4. Since we want the hypotenuse, you get the famous 3-4-5 triangle ratio. So the answer is 5 * 100 = 500.

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall, how high up the wall does the ladder reach? We have a right triangle, where the ladder is the hypotenuse, and we want the measurement of one leg. Set up the pythagorean theorem with these given items using our P[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=7&hypinput=25&pl=Solve+Missing+Side']ythagorean Theorem Calculator[/URL]. We get Side 1 = [B]24 feet.[/B]

A ladder is 25 ft long. The ladder needs to reach to a window that is 24 ft above the ground. How far away from the building should the bottom of the ladder be placed? We have a right triangle, where the ladder is the hypotenuse, and the window side is one side. Using our right triangle and the [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=24&hypinput=25&pl=Solve+Missing+Side']pythagorean theorem calculator[/URL], we get a length of [B]7 ft [/B]for the ladder bottom from the wall.

A ladder rests 2.5 m from the base of a house. If the ladder is 4 m long, how far up the side of the house will the ladder reach? We have a right triangle with the hypotenuse as 4, the one leg as 2.5 We want to solve for the other leg length. We use our [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=2.5&hypinput=4&pl=Solve+Missing+Side']right triangle solver[/URL] to get [B]3.122[/B]

A man stands at point p, 45 metres from the base of a building that is 20 metres high. Find the angle of elevation of the top of the building from the man. Draw a right triangle ABC where Side A is from the bottom of the building to the man and Side B is the bottom of the building to the top of the building. Using right triangle calculations, we want Angle A which is the angle of elevation. [URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=20&angle_b=&b=45&c=&pl=Calculate+Right+Triangle']Angle of Elevation[/URL] which is [B]23.9625°[/B]

A right triangle has legs of 9 feet and 12 feet. How long is the hypotenuse? A common right triangle ratio is 3:4:5 9 = 3 * 3 12 = 3 * 4 3 * 5 = 15, so we have [B]15 feet[/B]

A triangle has an area of 60 square inches and a base of 10 inches. What is its height? A = bh/2 b = 2A/h b = 2(60)/10 b = 120/10 b = [B]12 inches[/B]

a triangle has side lengths of 12,16, and 20 centimeters. is it a right triangle? First, we see if we can simplify. So we [URL='https://www.mathcelebrity.com/gcflcm.php?num1=12&num2=16&num3=20&pl=GCF']type GCF(12,16,20) [/URL]and we get 4. We divide the 3 side lengths by 4: 12/4 = 3 16/4 = 4 20/4 = 5 And lo and behold, we get a Pythagorean Triple of 3, 4, 5. So [B]yes, this is a right triangle[/B].

A triangular garden has base of 6 meters amd height of 8 meters. Find its area Area (A) of a triangle is: A = bh/2 Plugging in our numbers, we get: A = 6*8/2 A = [B]24 square meters[/B]

A young dad, who was a star football player in college, set up a miniature football field for his five-year-old young daughter, who was already displaying an unusual talent for place-kicking. At each end of the mini-field, he set up goal posts so she could practice kicking extra points and field goals. He was very careful to ensure the goalposts were each straight up and down and that the crossbars were level. On each set, the crossbar was six feet long, and a string from the top of each goalpost to the midpoint between them on the ground measured five feet. How tall were the goalposts? How do you know this to be true? The center of each crossbar is 3 feet from each goalpost. We get this by taking half of 6, since midpoint means halfway. Imagine a third post midway between the two goal posts. It has the same height as the two goalposts. From the center post, the string from the top of a goalpost to the base of the center post, and half the crossbar form and right triangle with hypotenuse 5 feet and one leg 3 feet. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=3&hypinput=5&pl=Solve+Missing+Side']Using the Pythagorean Theorem[/URL], the other leg -- the height of each post -- is 4 feet.

An equilateral triangle has three sides of equal length. What is the equation for the perimeter of an equilateral triangle if P = perimeter and S = length of a side? P = s + s + s [B]P = 3s[/B]

An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the measure of all 3 angles? Let the congruent angles measurement be c. And the non-congruent angle measurement be n. We're given: [LIST=1] [*]n = 2c + 16 <-- Twice means we multiply by 2, and more than means we add 16 [*]2c + n = 180 <-- Since the sum of angles in an isosceles triangle is 180 [/LIST] Substitute (1) into (2): 2c + (2c + 16) = 180 Group like terms: 4c + 16 = 180 [URL='https://www.mathcelebrity.com/1unk.php?num=4c%2B16%3D180&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]c = 41[/B] Substituting this value into Equation 1, we get n = 2(41) + 16 n = 82 + 16 [B]n = 98[/B]

Free Angle Ratio for a Triangle Calculator - Given an angle ratio for a triangle of a:b:c, this determines the angle measurements of the triangle.

Free Cevian Triangle Relations Calculator - Given a triangle with a cevian, this will solve for the cevian or segments or sides based on inputs

Chris walks 12 blocks north and then 16 blocks East. How far is his home from the park We've got a right triangle. If we divide 12 and 16 by 4, we get: 12/4 = 3 16/4 = 4 Since the hypotenuse is the distance from the home to the park, we have a classic 3-4-5 right triangle. So our hypotenuse is 5*4 = [B]20[/B]

Free Describe Two-Dimensional Shapes Calculator - Calculates the following:
Given a description of a 2D shape, it will return the shape (Circle, rectangle, square, triangle, etc.)

Free Equilateral Triangle Calculator - Given a side (a), this calculates the following items of the equilateral triangle:
* Perimeter (P)
* Semi-Perimeter (s)
* Area (A)
* altitudes (h_a,h_b,h_c)
* medians (m_a,m_b,m_c)
* angle bisectors (t_a,t_b,t_c)
* Circumscribed Circle Radius (R)
* Inscribed Circle Radius (r)

Free Geometric Mean of a Triangle Calculator - Given certain segments of a special right triangle, this will calculate other segments using the geometric mean

Given the rectangular prism below, if AB = 6 in., AD = 8 in. and BF = 24, find the length of FD. [IMG]http://www.mathcelebrity.com/images/math_problem_library_129.png[/IMG] If AB = 6 and AD = 8, by the Pythagorean theorem, we have BD = 10 from our [URL='http://www.mathcelebrity.com/pythag.php?side1input=6&side2input=8&hypinput=&pl=Solve+Missing+Side']Pythagorean Theorem[/URL] Calculator Using that, we have another right triangle which we can use the [URL='http://www.mathcelebrity.com/pythag.php?side1input=10&side2input=24&hypinput=&pl=Solve+Missing+Side']pythagorean theorem[/URL] calculator to get [B]FD = 26[/B]

In a video game, Shar has to build a pen shaped like a right triangle for her animals. If she needs 16 feet of fence for the shortest side and 20 feet of fence for the longest side, how many feet of fencing is needed for the entire animal pen? Using our [URL='https://www.mathcelebrity.com/righttriangle.php?angle_a=&a=&angle_b=&b=16&c=20&pl=Calculate+Right+Triangle']right triangle calculator[/URL]: Remaining side = 12 Total fencing needed is 16 + 20 + 12 = [B]48 feet of fencing[/B]

Free Isosceles Triangle Calculator - Given a long side (a) and a short side (b), this determines the following items of the isosceles triangle:
* Area (A)
* Semi-Perimeter (s)
* Altitude a (ha)
* Altitude b (hb)
* Altitude c (hc)

Juan runs out of gas in a city. He walks 30yards west and then 16 yards south looking for a gas station. How far is he from his starting point? Juan is located on a right triangle. We calculate the hypotenuse: 30^2 + 16^2 = Hypotenuse^2 900 + 256 = Hypotenuse^2 Hypotenuse^2 = 1156 Take the square root of each side: [B]Hypotenuse = 34 yards[/B]

Free Line Equation-Slope-Distance-Midpoint-Y intercept Calculator - Enter 2 points, and this calculates the following:
* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points
* Midpoint of the two points
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* 2 remaining angles of the rignt triangle formed by the 2 points
* y intercept of the line equation
* Point-Slope Form
* Parametric Equations and Symmetric Equations

Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.

Also allows for the entry of m and b to form the line equation

Free Pascal-Floyd-Leibniz Triangle Calculator - This generates the first (n) rows of the following triangles:
Pascal's Triangle
Leibniz's Harmonic Triangle
Floyd's Triangle

Put the number 123456789 exactly ones in the bubble so that each edge adds up to say number [B] Each side adds up to 17 [IMG]https://www.mathcelebrity.com/images/triangle_sum_17.png[/IMG] [/B]

Free Pythagorean Theorem Calculator - Figures out based on user entry the missing side or missing hypotenuse of a right triangle. In addition, the calculator shows the proof of the Pythagorean Theorem and then determines by numerical evaluation if the 2 sides and hypotenuse you entered are a right triangle using the Pythagorean Theorem

rectangle abcd prove: triangle adc is congruent to triangle bcd 1. Given: ABCD is a rectangle 2. AB = CD since opposite sides of rectangle are congruent 3. BC = AD since opposite sides of rectangle are congruent 4. AC = AC by the Reflexive Property of Equality 5. triangle ADC = triangle CBA by the Side-Side-Side (SSS) Property

Free Right Triangles Calculator - This solves for all the pieces of a right triangle based on given inputs using items like the sin ratio, cosine ratio, tangent ratio, and the Pythagorean Theorem as well as the inradius.

Running from the top of a flagpole to a hook in the ground there is a rope that is 9 meters long. If the hook is 4 meters from the base of the flagpole, how tall is the flagpole? We have a right triangle, with hypotenuse of 9 and side of 4. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=4&hypinput=9&pl=Solve+Missing+Side']Using our Pythagorean Theorem calculator[/URL], we get a flagpole height of [B]8.063[/B].

Free Special Triangles: Isosceles and 30-60-90 Calculator - Given an Isosceles triangle (45-45-90) or 30-60-90 right triangle, the calculator will solve the 2 remaining sides of the triangle given one side entered.

The base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of the triangle is less than 10 units. Write and solve an inequality that represents the possible area A of the triangle We're given: b=2/7A We're also told that b is less than 10. So we have: 2/7A < 10 2A/7 < 10 Cross multiply: 2A < 7 * 10 2A < 70 Divide each side of the inequality by 2 to isolate A 2A/2 < 70/2 Cancel the 2's on the left side and we get: A < [B]35[/B]

The distance between consecutive bases is 90 feet. An outfielder catches the ball on the third base line about 40 feet behind third base. How far would the outfielder have to throw the ball to first base? We have a right triangle. From home base to third base is 90 feet. We add another 40 feet to the outfielder behind third base to get: 90 + 40 = 130 The distance from home to first is 90 feet. Our hypotenuse is the distance from the outfielder to first base. [URL='https://www.mathcelebrity.com/pythag.php?side1input=130&side2input=90&hypinput=&pl=Solve+Missing+Side']Using our Pythagorean theorem calculator[/URL], we get: d = [B]158.11 feet[/B]

The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimeter of the triangle if its area is 3000. [LIST] [*]h = b + 70 [*]A = 1/2bh = 3000 [/LIST] Substitute the height equation into the area equation 1/2b(b + 70) = 3000 Multiply each side by 2 b^2 + 70b = 6000 Subtract 6000 from each side: b^2 + 70b - 6000 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=b%5E2%2B70b-6000%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get: b = 50 and b = -120 Since the base cannot be negative, we use b = 50. If b = 50, then h = 50 + 70 = 120 The perimeter is b + h + hypotenuse Using the [URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=70&angle_b=&b=50&c=&pl=Calculate+Right+Triangle']right-triangle calculator[/URL], we get hypotenuse = 86.02 Adding up all 3 for the perimeter: 50 + 70 + 86.02 = [B]206.02[/B]

The ratio of the measures of the 3 angles of a triangle is 1:2:3. What is the measure of the largest angle in degrees? Let the smallest angle be x. Then we have 3 angles based on the ratio: x, 2x, 3x We know the sum of the angles of a triangle equals 180. So we have: x + 2x + 3x = 180 6x = 180 Divide each side by 6: 6x/6 = 180/6 x = 30 The largest angle is 3(30) = [B]90 [MEDIA=youtube]l8Lc6YtK9dg[/MEDIA][/B]

The sides of a triangle are consecutive numbers. If the perimeter of the triangle is 240 m, find the length of each side Let the first side be n. Next side which is consecutive is n + 1 Next side which is consecutive is n + 1 + 1 = n + 2 So we have the sum of 3 consecutive numbers is 240. We type in [I][URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof3consecutivenumbersis240&pl=Calculate']sum of 3 consecutive numbers is 240[/URL][/I] into our search engine and we get: [B]79, 80, 81[/B]

The sum of the measures of two exterior angles of a triangle is 205. What is the measure of the third exterior angle? The sum of exterior angles for a triangle is 360. To find the third exterior angle, we take 360 - 205 = [B]155[/B].

Free Triangle Coordinate Items Calculator - Enter 3 points for the vertices of a triangle, and this will calculate the area of that triangle and the centroid.

Free Triangle Inequality Calculator - This calculator displays 2 scenarios
1) Enter 3 sides of a triangle, and it will determine if the side lengths satisfy the properties of the triangle inequality and form a triangle
2) Enter 2 sides of a triangle, and this will determine an acceptable range for the length of the 3rd side of a triangle so that the 3rd side respects the Triangle Inequality.

Triangle KLM has vertices at . k(-2,-2), l(10,-2), m(4,4) What type of triangle is KLM? [URL='https://www.mathcelebrity.com/slope.php?xone=-2&yone=-2&slope=+2%2F5&xtwo=10&ytwo=-2&pl=You+entered+2+points']Side 1: KL[/URL] = 12 [URL='https://www.mathcelebrity.com/slope.php?xone=10&yone=-2&slope=+2%2F5&xtwo=4&ytwo=4&pl=You+entered+2+points']Side 2: LM[/URL] = 8.4853 [URL='https://www.mathcelebrity.com/slope.php?xone=-2&yone=2&slope=+2%2F5&xtwo=4&ytwo=4&pl=You+entered+2+points']Side 3: KM[/URL] = 6.3246 Then, we want to find the type of triangle. Using our [URL='https://www.mathcelebrity.com/tribasic.php?side1input=12&side2input=8.4853&side3input=6.3246&angle1input=&angle2input=&angle3input=&pl=Solve+Triangle']triangle solver with our 3 sides[/URL], we get: [B]Obtuse, Scalene[/B]

Free Triangle Solver and Classify Triangles Calculator - Solves a triangle including area using the following solving methods
Side-Angle-Side (SAS) Side Angle Side
Angle-Side-Angle (ASA) Angle Side Angle
Side-Side-Angle (SSA) Side Angle Side
Side-Side-Side (SSS) Side Side Side
Area (A) is solved using Herons Formula
Law of Sines
Law of Cosines

Also classifies triangles based on sides and angles entered.

The triangle sum theorem states the sum of the three angles in a triangle equals 180 degrees. So if you're given two angles and need too find the 3rd angle, add the 2 known angles up, and subtract them from 180 to get the 3rd angle measure.

What kind of triangle? Do you have side lengths? I need more information.

A triangle with a perimeter of 120. What degree are the three sides?

Free Triangles Calculator - This lesson walks you through the basics of a triangle and shows you triangle types like acute, right, obtuse, scalene, isosceles, equilateral.

Tristan is building a slide for his kids. The ladder is 6 feet tall and the slide is 10 feet long. What is the distance between the ladder and the bottom of the slide? The answer is 8. We have a 3-4-5 triangle. But it's scaled by 2. 3 * 2 = 6 5 * 2 = 10 (hypotenuse-slide) 4 * 2 = [B]8[/B]

What is the area of a triangular parking lot with a width of 200m and a length of 100m? Area of a Triangle = bh/2 Plugging in our numbers, we get: Area of Parking Lot = 200(100)/2 Area of Parking Lot = 100 * 100 Area of Parking Lot = [B]10,000 sq meters[/B]