. The angle of depression of a car standing on the ground from the top of a 50 m high tower is 30°. The distance of the car from the base of the tower is:
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The angle of depression of a car standing on the ground from the top of a tower is 30 degree i.e. ∠ACB = 30°
Height of the tower = 75 m i.e. AB = 75 m
Now we are supposed to find the distance of the car from the base of the tower i.e. BC
In ΔABC
We will use trigonometric ratio
Tan\theta = \frac{Perpendicular}{Base}Tanθ=
Base
Perpendicular
Tan 30^{\circ}= \frac{AB}{BC}Tan30
∘
=
BC
AB
\frac{1}{\sqrt{3}}= \frac{75}{BC}
3
1
=
BC
75
BC= \frac{75}{\frac{1}{\sqrt{3}}}BC=
3
1
75
BC= 129.90BC=129.90
Hence the height if 120.90m
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