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=(opp)/(hyp)` (trigonometric formula)

On substituting the values we get,

`\Rightarrow sin(30^(\circ))=(20)/(AC)`

The value of sin 30 degree is 0.5

`\Rightarrow 0.5=(20)/(AC)\rightarrow AC=(20)/(0.5)\rightarrow AC=40 ft`