Question

A wall with a height of 20 feet is braced with a support post that forms a 30 degree angle with the top of the wall. What is the length of the support post?

Answer 1

The length of the support post is 40 ft.

Solution:

Given, the height of the wall is 20 ft; support post forms 30 degree

Refer the attached image

Let us name the triangle as ABC where AB is the wall (opposite side) of 20 ft and $\angle A$ is 30 degree ($\theta$) and AC is the length of the post.

To find: The length of the post (AC)

we know the formula, $sin\theta=\frac{opp}{hyp}$ (trigonometric formula)

On substituting the values we get,

$\Rightarrow sin(30^{\circ})=\frac{20}{AC}$

The value of sin 30 degree is 0.5

$\Rightarrow 0.5=\frac{20}{AC}\rightarrow AC=\frac{20}{0.5}\rightarrow AC=40 ft$