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

Answer:

B:  50 feet

Step-by-step 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,

$AC^2=AB^2+BC^2-2\times AB\times BC\times cos 30^{\circ}$

$=100^2+80^2-2\times 100\times 80\times \frac{\sqrt{3}}{2}$

$=10000+6400-8000\sqrt{3}$

$=2543.59353945$

$\implies AC=50.434051388\approx 50$

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

Option 'B' is correct.