Question

If you are 6 ft tall and stand 15 ft away from the bottom of a building that is 170 ft tall and look up to the roof, what is the angle of elevation from your head to the top of the building?

Answer 1

The angle of elevation from your head to the top of the building is 84.95°

Explanation:

Given : you are 6 ft tall and stand 15 ft away from the bottom of a building that is 170 ft tall .

We have to find the angle of elevation from your head to the top of the building.

Consider the figure below,

Where AB represent 170 ft tall building, C represents your head.

BC is the distance from the bottom of a building to you.

We have to find α the angle of elevation.

Using trigonometric ratio,

`\tan\theta=(Perpendicular)/(base)`

here,
`\tan\alpha=(AB)/(BC)`

Substitute , we get,

`\Rightarrow \tan\alpha=(170)/(15)`

`\Rightarrow \tan\alpha=11.33`

`\Rightarrow \alpha=\tan^(-1)(11.33)`

`\Rightarrow \alpha=84.95`

Thus, the angle of elevation from your head to the top of the building is 84.95°