Question

Patty Cake and Jim Nasium are flying a kite. Patty is 200 m away from Jim who is holding the kite. Facing Jim, Patty finds the angle of elevation of the kite is 40 degrees . If the kite string makes an angle of 85 degrees with the ground, find the amount of string let out by Jim.

Answer 1

Amount of string let out by Jim will be 156.9 m.

Explanation:

Distance between Jim and Patty = 200 m

Angle of elevation of the kite from Jim = 85°

Angle of elevation of the kite from Patty = 40°

Angle between the lines joining Jim and kite and Patty and the kite = 180° - (85 + 40)° = 55°

By applying Sine rule in the triangle formed by the kite, Jim and Patty,

`\frac{\text{sin}55}{200}=\frac{\text{sin}40}{x}`

x =
`\frac{200* \text{sin}40}{\text{sin55}}`

x = 156.94

≈ 156.9 m

Therefore, amount of string let out by Jim will be 156.9 m.