Math - Angle of Elevation and Depression

Question

You are in the middle of an island hopping with your friends when water suddenly starts to enter the boat. You and your friends have to think of a fast way to be safe and you noticed that there’s a nearby island with a lighthouse on the shore, but you are not sure how far it is from you. The angle of elevation of your boat to the top of the 210ft lighthouse is 62 degrees.

1.How far are you from the lighthouse?

2.Nearby boats noticed what was going on and rapidly went towards your boat. The closest boat to your boat has an angle of elevation of 42 degrees, assuming that the lighthouse, your boat, and the rescuing boat are aligned in a straight line

a.   How far was the rescuing boat from your boat? 

b.   How far was the rescuing boat from the lighthouse?

3.Which one is closer to your boat? The lighthouse or the other boat? Why?

Answer 1

Assuming that the lighthouse is 210 ft. tall to answer question No. 1 if you take the tan of 62 degrees ,

tan 62 degrees = 210/x, where x is the distance of the lighthouse from your boat and solve for x, you will know the distance of the lighthouse from your boat.

You will have to explain No.2 a little bit more.