Question

Fromthe top of the tower which is 240m high, if the angle of depression of a pointon the ground is 30°, then the distance of the point from the foot of the toweris

Answer 1

I used trigonometric ratios

Answer 2

Answer:

The distance between the point and foot of tower is 240√3 m.

Step-by-step explanation:

Given:

Height of the tower(AC) = 240m

Angle of depression(θ) = 30°

To find:

Distance between the point and foot of the tower(BC) =?

Solution:

As we can see from the figure, AP is parallel to BC. Therefore, the angle between the point and top of the tower will be equal to the angle of depression as they form alternate angles.

Therefore, ∠B = 30° and ∠C = 90°. Hence, ΔACB is a right-angled triangle.

Using trigonometric formulas, we get

tan(θ) = opposite side/ adjacent side

tan(B) = AC/BC

tan(30°) = 240/BC

1/√3 = 240/BC

BC = 240√3

Therefore, the distance of the point from the foot of the tower is 240√3 m.

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