from the top of a building 10m high the angle of depression of a stone lying on the horizontal ground is 60° . calculate the distance of the stone from the foot of the building
Mathematics · College · Tue Nov 03 2020
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Given:
Height of the building = 10m
Angle of Depression = 60°
Calculate the distance of the stone from foot of the building
Solution:
Picture out a right triangle with a height of 10 m, and given an angle 60°, we all know that opposite angles are congruent, meaning that the angle from the stone is also 60°. The distance can be calculated using SOHCAHTOA, or Sin = Opposite over Hypotenuse, Cos = Adjacent Over Hypotenuse, and Tan =Opposite Over Adjacent. Since we are given an Opposite side which is 10m (height of the building), in order to determine the distance from the adjacent side we use the trigonometric function tan.
Tanθ= opposite/adjacent
Tan 60° = 10 m/ A
A Tan60° = 10 m
Divide both sides by Tan 60°, in order to get the value of m.
A = 5.77m
The distance of the stone from the building is 5.77 m.