Learn how to apply the Pythagorean theorem to solve problems involving right triangles, including finding the hypotenuse or adjacent sides.
Extract
[...] m Exercise 1. Schema: B H C BC = 16 m 2. Observation : The height AH divise the base BC in two equal parts: Thus, AH form a rectangle triangle ABH with AB = 10 BH = 8 m et AH to be calculated. 3. Pythagorean Theorem: In a right triangle: (hypotenuse)2 = (adjacent side)2 + (opposite side)2 Here, the hypotenuse is AB, the horizontal side is BH, and the vertical side is AH. 4. Calculation of the height: 5. [...]
[...] It's always the longest side. ? The other two sides are the adjacent sides to the right angle. 3 The Pythagorean theorem In a right triangle: (hypotenuse)2 = (side 1)2 + (side 2)2 If ?ABC is rectangle in BC2 = AB2 + AC2 4 Different cases of figure In ?ABC rectangle in the basic formula is: BC2 = AB2 + AC2. It's this equality that we manipulate according to what we are looking for (the hypotenuse BC or a side AB / AC). [...]
[...] I H G Exercice 3 Consider a rectangle triangle GHI in H GI = 13, GH = 5 We want to calculate the length of the side HI. 1. Draw a diagram of the right triangle and indicate the known sides. 2. Recall the Pythagorean theorem. 3. Isolate HI in the formula. 4. Calculate the length of HI. Exercise 4 We want to place a ladder against a wall to reach a window. The distance between the foot of the ladder and the wall is 3 m. [...]
[...] - We are looking to determine the exact height of the roof. 1. Draw a diagram of the triangle indicating the area corresponding to the height we are looking for. 2. Observe the diagram: what does the height tracing give? 3. Recall the Pythagorean theorem. 4. Calculate the exact height of the roof. 7 Corrections Parenthesis: recall on powers Exercise Exercise Exercise 1. Schema: We draw a right triangle GHI rectangle in with GI = 13 and GH = 5. The unknown side is HI. 2. [...]
[...] Draw a diagram representing the situation: the wall, the ground, the ladder and the window. 2. Recall the Pythagorean theorem. 3. Calculate the length of the ladder. Exercise 5 You must build a ramp for a wheelchair. The drop (height) to be overcome is 0.5 meters. The construction standards guide indicates that the length of the ramp on the ground must be 5 times its height. 1. What is the length of the ramp on the ground? 2. Draw a diagram representing the situation (the ground, the ramp, the height to be overcome). [...]
