Question

Sitting on a park bench you see a swing that is 100 feet away and a slide that is 60 feet away. The angle between them is 30 degrees . What is the approximate distance between the swing and the slide

Answer 1

Answer: The approximate distance between the swing and the slide is 56.21 feet.

Step-by-step explanation:

Since we have given that

Distance between bench and swing = 100 feet

Distance between bench and slide = 60 feet

Angle between them is given by

$30\textdegree$

So, we will use "Cosine law" to get the distance between the swing and the slide i.e.,

$c^2=a^2+b^2-2ab\cos\theta\\\\c^2=100^2+60^2-2\times 60\times 100\cos30\textdegree\\\\c^2=10000+3600-12000\cos30\textdegree\\\\c^2=13600-12000\times 0.87\\\\c^2=13600-10440\\\\c^2=3160\\\\c=\sqrt{3160}\\\\c=56.21\ feet$

Hence, the approximate distance between the swing and the slide is 56.21 feet.