Question

The roof of a house is the shape of an isosceles right triangle as shown in the diagram below.

A right triangle is shown. An altitude is drawn from the right angle to the opposite side to form another right angle. The length of the altitude is h. The length of one of the sides is 10.

What is the height of the roof, h?

5 ft
5 StartRoot 2 EndRoot ft
5 StartRoot 3 EndRoot ft
StartFraction 5 StartRoot 2 EndRoot Over 2 EndFraction ft

Answer 1

In a 45-45-90 (isosceles right) triangle with legs 10, the hypotenuse is 10√2. The altitude from the right angle to the hypotenuse equals (product of the legs)/(hypotenuse) = (10·10)/(10√2) = 10/√2 = 5√2.

So h = 5√2 ft.