Question

the angle of depression of a car standing on the ground from the top of a 66 m tower is 30° .find the distance of a car from the base of the tower

Answer 1

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Answer 2

GIVEN:

• Angle of depression of the car = 30°
• Height of the tower = 66 m

TO FIND:

• What is the distance of the car from the base of the tower ?

SOLUTION:

Here,

Height of the tower = 66 m

Let the distance of the car from B to C be 'x' m

In ∆ABC, ∠ACB = 30°

We know that,

$\bf{ tan\theta = \dfrac{Perpendicular}{Base}}$

So,

$\rm{\longmapsto tan \: 30\degree = \dfrac{AB}{BC}}$

$\rm{\longmapsto \dfrac{1}{\sqrt{3}} = \dfrac{66}{x}}$ [ tan 30° = 1/√3 ]

$\bf{\longmapsto x = 66\sqrt{3} \: m}$

❝ Hence, the distance of the car from the tower is 66√3 m ❞

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✯ IDENTITIES ✯

➾ sin²θ + cos²θ = 1

➾ 1 + tan²θ = sec²θ

➾ 1 + cot²θ = cosec²θ