Answer:
The angle of elevation from your head to the top of the building is 84.95°
Step-by-step explanation:
Given : you are 6 ft tall and stand 15 ft away from the bottom of a building that is 170 ft tall .
We have to find the angle of elevation from your head to the top of the building.
Consider the figure below,
Where AB represent 170 ft tall building, C represents your head.
BC is the distance from the bottom of a building to you.
We have to find α the angle of elevation.
Using trigonometric ratio,
[tex]\tan\theta=\frac{Perpendicular}{base}[/tex]
here, [tex]\tan\alpha=\frac{AB}{BC}[/tex]
Substitute , we get,
[tex]\Rightarrow \tan\alpha=\frac{170}{15}[/tex]
[tex]\Rightarrow \tan\alpha=11.33[/tex]
[tex]\Rightarrow \alpha=\tan^{-1}(11.33)[/tex]
[tex]\Rightarrow \alpha=84.95[/tex]
Thus, the angle of elevation from your head to the top of the building is 84.95°
