The angle of elevation of a man standing on a road to the top of a building is 60°. If the height of the building is 30 feet, find the distance between the man and the base of the building.
Answers
Answer
The distance is 17.32 feet
Step-by-step explanation:
Let the distance between the man and the base of the building be 'x' feet
The angle of elevation to the top of the building is 60°
So , let he height of man be 'y' feet
So , The reaming distance is (30-y) feet
The building will be opposite side to the angle and therefore will be the perpendicular
The distance is the adjacent side and therefore will be the base
So , we have relation between base and perpendicular
So , we will use the 'tangent'
Tan ø = Perpendicular / Base
As given -
ø (Angle) = 60°
Perpendicular = (30-y) feet
Base = ?
Tan 60° = (30-y) / x
root 3 = (30-y) / x
x = (30-y) / root 3 feet
If the height of the man is not considered in the question we will take y=0
x = (30-0) / root 3
= 30 / root 3
= 10 root 3
= 10 × 1.732 = 17.32 feet (approx)
So, the distance from the man to the base of the building is 17.32 feet .
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