# Solution - Heights and Distances

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ConceptHeights and Distances

#### Question

When the sun is 30º above the horizontal, Find the length of shadow cast by a building 50m high

#### Solution

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A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower the angle of elevation of the top of the tower is 60°. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the canal.

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A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.

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The angle of depression of a car parked on the road from the top of a 150 m high tower is 30°. The distance of the car from the tower (in metres) is

(A) 50sqrt3

(B) 150sqrt 3

(C) 150sqrt2

(D) 75

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If the angle of elevation of cloud from a point 200 m above a lake is 30º and the angle of depression of its reflection in the lake is 60º, then find the height of the cloud above the lake

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The elevation of a tower at a station A due north of it is α and at a station B due west of A is β. Prove that the height of the tower is \frac{AB\sin \alpha \sin \beta }{\sqrt{\sin^{2}\alpha -\sin ^{2}\beta

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#### Reference Material

Solution for concept: Heights and Distances. For the course 8th-10th CBSE
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