Answer:
The angle of elevation of his ladder is
.
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
be the angle of elevation of his ladder.
Then apply trigonometry,
![\tan\theta = \frac{\text{Perpendicular}}{\text{Base}}](https://tex.z-dn.net/?f=%5Ctan%5Ctheta%20%3D%20%5Cfrac%7B%5Ctext%7BPerpendicular%7D%7D%7B%5Ctext%7BBase%7D%7D)
![\Rightarrow \tan\theta=\frac{\text{height of building reached by ladder}}{\text{distance between ladder and building}}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Ctan%5Ctheta%3D%5Cfrac%7B%5Ctext%7Bheight%20of%20building%20reached%20by%20ladder%7D%7D%7B%5Ctext%7Bdistance%20between%20ladder%20and%20building%7D%7D)
![\Rightarrow\tan\theta=\frac{50}{30}=1.67\\\\\Rightarrow\theta=\tan^{-1}(1.67)\\\\\Rightarrow\ x=59.03^{\circ}\approx59^{\circ}](https://tex.z-dn.net/?f=%5CRightarrow%5Ctan%5Ctheta%3D%5Cfrac%7B50%7D%7B30%7D%3D1.67%5C%5C%5C%5C%5CRightarrow%5Ctheta%3D%5Ctan%5E%7B-1%7D%281.67%29%5C%5C%5C%5C%5CRightarrow%5C%20x%3D59.03%5E%7B%5Ccirc%7D%5Capprox59%5E%7B%5Ccirc%7D)
Therefore, The angle of elevation of his ladder is
.
Refer the attached figure below.