Question

A hot-air balloon is sighted at the same time by two friends who are 1.0 mile apart on the same side of the balloon. the angles of elevation from the two friends are 20.5° and 25.5°. how high is the balloon? (young 487) young, cynthia y. precalculus: with limits, 2nd edition. wiley, 2014-01-06. vitalbook file.

Answer 1

Tan 25.5 = h/x

Tan 20.5 = h / x+1

x tan 25.5 = (x+1) tan 20.5

x 0.476975532 = (x+1) 0.373884679

0.476975532x = 0.373884679x + 0.373884679

Deduct both sides by .373884679

0.103090853x = 0.373884679

x = 3.6267 is the first person.

Add one to get for the second person

X = 4.6267