Question

Letry. 14 Chapter 9: Chapter 9 rest Chapter Test

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

Answer 1

7.1 cm

Explanation:

:D

Answer 2

h = 7.1 cm

Explanation:

To find the height of the triangle, we can first find the area of the triangle using the Heron's formula:

`S = √(p(p-a)(p-b)(p-c))`

Where a, b and c are the sides of the triangle and p is the semi perimeter of the triangle:

`p = (a+b+c)/(2) = (15 + 8 + 17 )/(2) = 20\ cm`

So the area of the triangle is:

`S = √(20(20-15)(20-8)(20-17))`

`S = 60\ cm^2`

Now, to find the height, we can use the following equation for the area of the triangle:

`S = base * height/2`

The height draw in the figure is relative to the side of 17 cm, so this side is the value of base used in the formula. So we have that:

`60 = 17 * h/2`

`h = 120/17`

`h = 7.06\ cm`

Rounding to the nearest tenth, we have h = 7.1 cm