Question

the roof of a house is the shape of an isosceles right triangle as shown in the diagram below. what is the height of the roof, h? 5 ft 5√2 ft 5√3 ft 5√2/2 ft

Explanation:

Step1: Use Pythagorean theorem for isosceles right - triangle.

In an isosceles right - triangle, if the hypotenuse is $c$ and the legs are $a$ and $b$ (and $a = b$), $c^{2}=a^{2}+b^{2}=2a^{2}$. Given $c = 10$, then $10^{2}=2a^{2}$, so $a^{2}=50$, $a = 5\sqrt{2}$. The height $h$ is half of the hypotenuse of the smaller isosceles right - triangle formed, and the hypotenuse of the smaller one is the leg of the larger one. So $h = 5\sqrt{2}\div\sqrt{2}=5\sqrt{2}$ ft.

Answer:

$5\sqrt{2}\text{ ft}$