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.

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eudora eudora · Answer 1 · 2020-06-12T20:28:26+02:00

Answer:

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

Step-by-step 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,

[tex]\frac{\text{Sin}55}{200}=\frac{\text{Sin}40}{x}[/tex]

x = [tex]\frac{200\times \text{Sin}40}{\text{Sin}55}[/tex]

x = 156.94 m

≈ 156.9 m

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