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
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.