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

Answer 1

Answer:

5 StartRoot 2 EndRoot ft its B

Step-by-step explanation:

Answer 2

The height of the roof is 5 StartRoot 2 EndRoot ft

Isosceles right triangle

Since the triangle is isosceles, hence the base angles will be 45 degrees

Using the SOH CAH TOA identity;

• Cos 45 = adj/hyp

Given

• Adj = h
• Hyp = 10

Substitute

Cos 45 = h/10

h = 10cos45

h = 10 * 1/√2

h = 5√2

Hence the height of the roof is 5 StartRoot 2 EndRoot ft

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