Question

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° B) 58° C) 59° D) 60°

Answer 1

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

the angles measure is 59 degrees

Answer 2

Answer: $59^{\circ}$

Step-by-step explanation:

Consider that ladder is making a right triangle with the burning building.

Let x be the angle of elevation of his ladder.

Then $\Rightarrow\tan\ x=\frac{\text{height of building reached by ladder}}{\text{distance between ladder and building}}\\\\\Rightarrow\tan\ x=\frac{50}{30}=1.67\\\\\Rightarrow\ x=\tan^{-1}(1.67)\\\\\Rightarrow\ x=59.03^{\circ}\approx59^{\circ}$

Thus, the angle of elevation of his ladder is $59^{\circ}$