(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. - Noon Academy

(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.

ML Agarwal Heights and distances class 10 Maths

(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.

Solution:

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.

i

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