Question

you are flying a kite at an angle of 70 degrees. you have let out a total of 400ft of string and are holding the reel steady 4 feet above the ground. a friend watching the kite estimates that the angle of elevation to the kite is 85 degrees. how far from your friend are you standing?

Answer 1

170.466 feet

Explanation:

Given that the kite had an angle of elevation of 70 degrees and 4 ft above the ground.

Using sine values, we find that the height of the kite above the reel would be

`h = 400 sin 70=379.88`

Total height from the earth = 379.88+4 = 383.88 ft.

The friend estimates the angle of elevations as 85 degrees

i.e. if d is the distance from the kite position, then we have

d=383.88 cot 85

=33.586 ft

Distance of you from the kite
`= 400 cos 70 = 136.8 ft`

Distnce between friend and you = 136.88+33.586

= 170.466 feet

Answer 2

Answer: 170 ft away

First, find the height of the kite from the ground:

h + 4 = 400 sin 70
h + 4 = 379.88 ft (from the ground)

Then, my distance to the directly downwards of where the kite is flying is:

d = 400 cos 70
= 136.8 ft

Then the distance of my friend from me:

D = 136.8 ft + (379.87) tan 85
= 170 ft