Question

a roof support is built according to the diagram shown below.
what is the height of the roof in yards?
36
12√3
18√2
18

Explanation:

Step1: Analyze the triangle

The given triangle is an isosceles triangle (with two angles of \(30^{\circ}\)) divided into two right - angled triangles by the height. The base of each right - angled triangle is \(\frac{72}{2}=36\) yards.

Step2: Use trigonometric ratio

In a right - angled triangle with angle \(30^{\circ}\), \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here \(\theta = 30^{\circ}\), adjacent side \(= 36\) yards and opposite side is the height \(h\) of the roof.
We know that \(\tan30^{\circ}=\frac{h}{36}\). Since \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\), we have \(h = 36\times\tan30^{\circ}\).

$$h=36\times\frac{1}{\sqrt{3}}=\frac{36}{\sqrt{3}}=\frac{36\sqrt{3}}{3}=12\sqrt{3}$$

Answer:

\(12\sqrt{3}\) (the second option)