Word problem

Question

You need to determine the length of a tunnel drilled through a lunar peak at the center of a crater. From a point outside of the crater on the ground, you run ropes to the ends of the tunnel. The first ropes distance is 24.5 meters and the second ropes distance is 21.2 meters. The two ropes meet at an angle of 68D. What is the length of the tunnel? 

Answer 1

If you draw this out, you see that you have a triangle formed by the ropes and the tunnel.  You know the length of the ropes and the angle between them.  You want to find the other side of the triangle, opposite the angle you know.

 

That's a perfect example for the law of cosines.

 

c² = a² + b² - 2ab cos C

c² = 24.5² + 21.2² - 2 * 24.5 * 21.2 cos 68

c² = 600.25 + 449.44 - 389.14

c² = 660.55

c = 25.7 meters