The corporate office building is 50m high and angle of elevation at top of building is 52° when seen from a point on level groun
d. The distance between point and foot of the building is
1 answer:
Answer:
39.06 m
Step-by-step explanation:
Given that,
Height of the building, h = 50 m
The angle of elevation at top of building is 52° when seen from a point on level ground.
We need to find the distance between point and foot of the building. Let the distance be d. Using trigonometry to find it. So,
![\tan\theta=\dfrac{P}{B}](https://tex.z-dn.net/?f=%5Ctan%5Ctheta%3D%5Cdfrac%7BP%7D%7BB%7D)
Where
P is perpendicular
B is base.
So,
![\tan\theta=\dfrac{h}{d}\\\\d=\dfrac{h}{\tan\theta}\\\\d=\dfrac{50}{\tan(52)}\\\\d=39.06\ m](https://tex.z-dn.net/?f=%5Ctan%5Ctheta%3D%5Cdfrac%7Bh%7D%7Bd%7D%5C%5C%5C%5Cd%3D%5Cdfrac%7Bh%7D%7B%5Ctan%5Ctheta%7D%5C%5C%5C%5Cd%3D%5Cdfrac%7B50%7D%7B%5Ctan%2852%29%7D%5C%5C%5C%5Cd%3D39.06%5C%20m)
So, the distance between point and foot of the building is 39.06 m
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