Question

The Statue of Unity, situated in Gujarat, is the world’s largest Statue which stands over a 58 m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of the Statue of Unity using it. He noted the following observations from two places: Situation I: The angle of elevation of the top of Statue from Place A, which is `80sqrt3` m away from the base of the Statue is found to be 60°. Situation II: The angle of elevation of the top of Statue from Place B, which is 40 m above the ground, is found to be 30° and entire height of the statue, including the base, is found to be 240 m.

Based on the given information, answer the following questions:

1. Represent Situation I with the help of a diagram.   (1)
2. Represent Situation II with the help of a diagram.  (1)
3. 1. Calculate the height of Statue excluding the base and also find the height including the base with the help of Situation I.   (2)
                                     OR
   2. Find the horizontal distance of point B (Situation II) from the Statue and the value of tan α, where α is the angle of elevation of the top of the base of the Statue from point B.  (2)

Answer 1

i. Situation I

ii. Situation II

iii. a. From Situation I diagram,

QA = Distance between statue and point A = `80sqrt3` m

Height including the base

tan 60° = `(TQ)/(80sqrt3)`

`sqrt3 = (TQ)/(80sqrt3)`

`sqrt3 xx 80sqrt3` = TQ

TQ = 240 m

Height of statue excluding base = 240 − 58

= 182 m

OR

b. From Situation II diagram,

In ΔTRB,

tan 30° = `(200)/(RB)`

`1/sqrt3 = 200/(RB)`

RB = `200sqrt3` m

TQ = TR + RQ

240 = TR + 40

240 − 40 = TR 

200 = TR

tan α = `(PR)/(RB)`

= `18/(200sqrt3) xx sqrt3/sqrt3`

= `(18sqrt3)/(200 xx 3)`

= `(3 xx 1.732)/100`

= `5.196/100`

tan α = 0.05196

α = tan⁻¹ (0.05196)