Question

In order to use a ladder safely, the angle that the ladder forms with the ground should not exceed 70 degree. If you have a ladder that is 16 ft. long, what is the maximum height on the wall of a building that the ladder will safely reach? Round your answer to the nearest thousandth.

Answer 1

Maximum safe height can be reached by ladder = 15.03. ft

Explanation:

Given,

Let's assume the maximum safe height of wall = h

angle formed between ladder and ground = 70°

length of ladder = 16 ft

From the given data, it can be seen that ladder will form a right angle triangle structure with the wall

So,from the concept of trigonometry,

`Sin70^o\ =\ \frac{\textrm{maximum safe height of wall}}{\textrm{length of ladder}}`

`=>Sin70^o\ =\ (h)/(16\ ft)`

`=>\ h\ =\ 16* Sin70^o`

=> h = 16 x 0.9396

=> h = 15.03 ft

So, the maximum safe height that can be reached by the ladder will be 15.03 ft.