Trigonometry Question

Question

Two iron wrecking balls with a height of 5 ft. Each are hanging straight down on ropes, one 12 ft. long and the other 8 ft. long. The balls are 28 ft. apart. If they are swung to meet, what will the angle “theta” be between them?

Answer 1

I see Mark M provided an equation, but unfortunately, solving that equation doesn't yield an angle; it yields a domain error: no triangle exists with sides 8, 15, and 28.

At the same time, I'm not sure there is a numerical solution to the problem as presented: wrecking balls 28 feet apart need more rope if they are to be able to meet.

Answer 2

Drew and label a diagram

θ represents the angle between the two balls

Use the Law of Cosines

28² = 8² + 15² - (2)(8)(15) cos θ