Question

A statue. 1.6 m 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
​

Answer 1

Answer:

From triangle BCD

tan45 = BC/CD

=> 1 = BC/CD

=> CD = BC

Again triangle ACD

tan60 = AC/CD

=> √3 = (AB + BC)/CD

=>√3*CD = AB + BC

=> √3BC = 1.6 + BC

=> √3BC - BC = 1.6

=> (√3 - 1)BC = 1.6

=> BC = 1.6/ (√3 - 1)

=> BC ={1.6* (√3 + 1)}/{(√3 - 1)*(√3 + 1)}

=> BC ={1.6* (√3 + 1)}/2

=> BC = 0.8 *(√3 + 1)

So height of pedestal is 0.8 *(√3 + 1)

Answer 2

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Let AB be the height of statue.

D is the point on the ground from where the elevation is taken.

To Find: Height of pedestal = BC = AC – AB

From figure,

In right triangle BCD,

↦ tan 45° = BC/CD

↦ 1 = BC/CD

↦ BC = CD ….(1)

Again,

In right ΔACD,

tan 60° =√3 = AB+BC/CD

↦ √3 CD = 1.6 + BC

↦ √3BC = 1.6 + BC (using equation (1)

↦ √3BC – BC = 1.6

↦ BC(√3-1) = 1.6

↦ BC = 1.6/(√3-1) m

BC=0.8(√3+1)

Thus, the height of the pedestal is 0.8(√3+1) m.