Question

Read the following passage and answer the questions given below.

Qutub Minar, located in South Delhi, India was built in the year 1193. It is 72 m high tower. Working on a school project, Charu and Daljeet visited the monument. They used trigonometry to find their distance from the tower. Observe the picture given below. Points C and D represent their positions on the ground in line with the base of tower, the angles of elevation of top of the tower (Point A) are 60° and 45° from points C and D respectively.

1. Based on the above information, draw a well-labelled diagram.
2. Find the distances CD, BC and BD. [use `sqrt(3)` = 1.73]

Answer 1

1.

2.

In ΔABC, tan 60° = `("AB")/("BC")`

⇒ `sqrt(3) = 72/("BC")`

⇒ BC = `72/sqrt(3) = 24sqrt(3)`

= 24 × 1.73

⇒ BC = 41.52 m

In ΔABD, ∠B = 90°

tan 45° = `("AB")/("BD")`

BD = AB

BD = 72 m

Now, CD = BD – BC

= 72 – 41.52

CD = 30.48 m