Question

A boy standing on a horizontal plane is flying a kite with a string of length 60 m, at an angle of elevation of 30°. Another boy standing on the roof of a 20 m high building, finds the angle of elevation of same kite to be 45°. If both the boys are on opposite sides of the kite, find the distance of the first boy from the base of the building. Also, find the height of the Kite from the ground. (Use `sqrt3 = 1.73`)

Answer 1

Given: String length = 60 m

Angle of elevation = 30°

In a right triangle,

sin 30° = `h/60`

`1/2 = h/60`

h = 30 m

The horizontal distance of the kite from the first boy:

cos 30° = `("base")/60`

`sqrt3/2 = ("base")/60`

base = `60 xx sqrt3/2`

= `30sqrt3`

= 30 × 1.73   

= 51.9 m

Height of building = 20 m

Height of kite = 30 m

Vertical difference = 30 − 20

= 10 

Angle of elevation = 45°

tan⁡45° = `"opposite"/"adjacent"`

1 = `10/h` 

h = 10 m

Total distance between the first boy and the base of the building

= 51.9 + 10

= 61.9 m