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# (i) In the adjoining figure, the angle of elevation from a point P of the top of a tower QR, 50 m high is 600 and that of the tower PT from a point Q is 300. Find the height of the tower PT, correct to the nearest metre. (ii) From a boat 300 metres away from a vertical cliff, the angles of elevation of the top and the foot of a vertical concrete pillar at the edge of the cliff are 550 40’ and 540 20’ respectively. Find the height of the pillar correct to the nearest metre.

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sir this is the question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances
we have given a figure and  In the adjoining figure, the angle of elevation from a point P of the top of a tower QR, 50 m high is 600 and that of the tower PT from a point Q is 300.

we have to Find the height of the tower PT, correct to the nearest metre.
(ii) From a boat 300 metres away from a vertical cliff,
the angles of elevation of the top and the foot of a vertical concrete pillar at the edge of the cliff are 550 40’ and 540 20’ respectively.
Find the height of the pillar correct to the nearest metre.

question no 14 , heights and distances , ICSE board

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### 1 Answer

1. Consider CB as the cliff and AC as the pillar

D as the boat which is 300 m away from the foot of the cliff BD = 300 m

Angle of elevation of the top and foot of the pillar are 550 40’ and 540 20’

Take CB = x and AC = y

In a right triangle CBD

tan θ = CB/BD

Substituting the values

tan 540 20’ = x/300

So we get

1.3933 = x/300

By cross multiplication

x = 300 × 1.3933

x = 417.99 m

In a right triangle ABD

tan θ = AB/BD

Substituting the values

(x + y)/ 300 = 1.4641

By cross multiplication

x + y = 1.4641 × 300 = 439.23

Substituting the value of x

y = 439.23 – 417.99 = 21.24 m = 21 m

Hence, the height of pillar is 21 m.

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