Question

11) A fireman is standing 30 m directly west of a burning building. His ladder reaches 50 m up the side of the building. What is the angle of elevation (to the closest degree) of his ladder? A) 48°

Answer 1

tan of the angle = opposite side / adjacent = 50/30 = 1 .667

the angles measure is 59 degrees

Answer 2

Answer:

The angle of elevation of his ladder is $59^{\circ}$.

Step-by-step explanation:

Given : A fireman is standing 30 m directly west of a burning building. His ladder reaches 50 m up the side of the building.

To find :  What is the angle of elevation (to the closest degree) of his ladder?

Solution :

Let us assume that ladder is making a right triangle with the burning building                            

Let $\theta$  be the angle of elevation of his ladder.

Then apply trigonometry,

$\tan\theta = \frac{\text{Perpendicular}}{\text{Base}}$

$\Rightarrow \tan\theta=\frac{\text{height of building reached by ladder}}{\text{distance between ladder and building}}$

$\Rightarrow\tan\theta=\frac{50}{30}=1.67\\\\\Rightarrow\theta=\tan^{-1}(1.67)\\\\\Rightarrow\ x=59.03^{\circ}\approx59^{\circ}$

Therefore, The angle of elevation of his ladder is $59^{\circ}$.

Refer the attached figure below.