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 t…

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asked Oct 16, 2019 129k views

2 Answers

Justo · Answer 1 · 2019-10-22T18:36:33+0000

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.