Question

Sitting on a park bench, you see a swing that is 100 feet away and a slide that is 80 feet away. The angle between them is 30 degrees. What is the approximate distance between the swing and the slide?

Answer 1

ANSWER:50

Explanation:

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Answer 2

We are given : Distance of the swing = 100 feet.

Distance of slide = 80 feet.

Angle between swing and slide = 30 degrees.

We need to find the distance between the swing and the slide.

Distance of swing, distance of slide and distance between the swing and the slide form a triangle.

We can apply cosine law to find the distance between the swing and the slide.

c^2 = a^2 +b^2 - 2ab cos C

c^2 = 100^2 +80^2 - 2(100)(80) cos 30°

c^2 = 10000 + 6400 -2* 8000
`(\frac{√(3)} 2)}`

c^2 = 16400 - 8000
`√(3)`

c^2 = 16400 - 13856

c^2 = 2544

`c =√(2544)`

c= 50.44

c = 50 feet approximately.

Therefore, the approximate distance between the swing and the slide is 50 feet.