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A highway leads to the foot of 300 m high tower. An observatory is set at the top of the tower. It sees a car moving towards it at an angle of depression of $30 °$ After 15 seconds angle of depression becomes $60 °$ Find the distance traveled by car during this time.

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346.4 m

364.6 m

300 m

426.3 m

answer is B.

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Detailed Solution

Given that a highway leads to the foot of 300 m high tower.
We have to find the distance traveled by the car.
The value for the trigonometric identities can be evaluated by using the right-angled triangle the value for can be expressed as

tan θ = opposite adjacent

Suppose the height of the tower be OD=300m.
Then, by using the figure geometry:
Question Image

In triangle DOB, tan θ = O D O B ⇒ tan 30 ° = 300 O B ⇒ 13 = 300 O B ∴ O B = 519.6 m

Similarly, in the triangle DOA, tan 60 ° = D O O A ⇒ 3 = 300 O A ∴ O A = 173.2 m

Thus, the distance traveled by the car is,

A B = O B − O A ⇒ A B = 519.61 − 173.2 ⇒ A B = 346.4. m

The distance traveled is 346.4m
Therefore, the correct option is 2.

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