Question

A kite on a 160-foot string is caught on a pole. When the full length of the string is stretched in a straight line to the ground, it touches the ground a distance of 50 feet from the bottom of the pole. The string forms an angle of _______° with the ground when it is stretched like this.

Answer 1

String form an angle of 18.2° with the ground.

Explanation:

Given: Length of the string of a kite = 160 ft.

Kite stuck on pole at height of = 50 ft.

We need to find: Measure of angle formed by string of kite with ground.

Attached figure showing the given situation.

let α be the required angle.

In ΔABC,

using trigonometric ratio,

`sin\,\aplha=(AB)/(AC)`

`sin\,\aplha=(50)/(160)`

`sin\,\aplha=(5)/(16)`

`sin\,\aplha=0.3125`

`\aplha=sin^(-1)(0.3125)`

`\alpha=18.20995686428301`

`\alpha=18.21`

Therefore, String form an angle of 18.2° with the ground.