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

Length of the string let out by Jim is 156.9 m.

Explanation:

From the figure attached,

Jim observes the angle of elevation of the kite = 85°

And Patty observes the angle of elevation of the kite = 40°

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

Distance between Jim and Patty = 200 m

Let the length of the string between Jim and the kite = x meters

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

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

x =
`\frac{200* \text{Sin}40}{\text{Sin}55}`

x = 156.94 m

≈ 156.9 m

Therefore, length of the kite string from Jim and the kite is 156.9 m.