Question

A roof has a cross section that is a right triangle. The diagram shows the approximate dimensions of this cross section. Find the height h of the roof. Round your answer to the nearest tenth.

Answer 1

25ft :)

Explanation:

Answer 2

The height of the roof is 25 ft.

Explanation:

Consider the right angled triangle BCD.

Determine the measure of side BD using the Pythagoras theorem

`BD^(2)=BC^(2)+CD^(2)\\\\BD=\sqrt{BC^(2)+CD^(2)}\\\\=\sqrt{10^(2)+5^(2)}\\\\=√(125)`

Compute the measure of angle x as follows:

`tan\ x=(BC)/(CD)\\\\tan\ x=(10)/(5)\\\\tan\ x=2\\\\x=tan^(-1)2\\\\x=63.4`

Now consider the triangle ABD.

The hypotenuse AD is the height of the roof.

Determine the measure of side AD as follows:

`cos\ x=(BD)/(AD)\\\\cos\ 63.4=(√(125))/(AD)\\\\0.4478=(√(125))/(AD)\\\\AD=(√(125))/(0.4478)\\\\AD=24.967\\\\AD\approx 25`

Thus, the height of the roof is 25 ft.