Question

A ladder that is 30 ft long needs to reach 27 ft up a building. What should the angle off of the vertical be?

Answer 1

The angle off to the vertical is 25.8°

Step-by-step explanation:

Given as :

The length of the ladder = l = 30 ft

The height of the building = h = 27 ft

Let The angle off to the vertical = Ф°

According to question

Cos angle = $\dfrac{base}{perpendicular}$

i.e  Cos Ф = $\dfrac{h}{l}$

Or,  Cos Ф = $\dfrac{27 ft}{30 ft}$

∴     Cos Ф = $\dfrac{9}{10}$

i.e    Cos Ф = 0.9

Or,  Ф = $Cos^{-1}$ 0.9

or,   Ф = 25.8°

So, The angle off to the vertical = Ф= 25.8°

Hence, The angle off to the vertical is 25.8°   Answer