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 )
Share
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