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 30°. What I the approximate distance between the swing and the slide?

A: 24 feet
B: 50 feet
C: 148 feet
D: 161 feet

Answer 1

B: 50 feet

Explanation:

Let A represents the location of the swing, B represents the location of bench and C represents the position of slide,

According to the question,

AB = 100 ft,

BC = 80 ft,

m∠ABC = 30°,

By the cosine law,

`AC^2=AB^2+BC^2-2* AB* BC* cos 30^(\circ)`

`=100^2+80^2-2* 100* 80* (√(3))/(2)`

`=10000+6400-8000√(3)`

`=2543.59353945`

`\implies AC=50.434051388\approx 50`

Hence, the approximately distance between the swing and the slide is 50 ft.

Option 'B' is correct.