CBSE 10th Class Mathematics

Past year question paper

Year 2020

SET 1, Code Number – 30/5/1

Question Number – 39

trigonometric function

use trigonometric relation

sin, cos and tan relation

Deepak BoraNewbie

# A statue 1.6m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal. (Use √3 = 1.73 )

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As per figure, BC = h m

In right triangle ACP,

tan 60° = AC / PC

√3 = [AB + BC] / PC

√3 = [1.6 + h] / PC …. (1)

In right triangle BCP,

tan 45° = BC / PC

1 = h / PC … (2)

Dividing (1) by (2), we get

√3 / 1 = [1.6 + h] / h

h√3 = 1.6 + h

h[√3 – 1] = 1.6

h = 1.6 / [√3 – 1]

h = { ( 1.6 / [√3 + 1] ) / ( [√3 – 1] [√3 + 1] ) )

h = 0.8 [√3 + 1]

h=0.8(1.73+1)=0.8 x 2.73 =2.184 m

Hence, the height of the pedestal is 2.184 m