From an observation deck on top of a lighthouse , the angles of depression to two boats that are known to be 350 feet apart are 12° and 25°. How tall is the tall is the lighthouse?

Answer 1

Draw and label a diagram.

h represents the height of the tower

x represents the distance between tower and closer boat

h / x = tan 25°

h = x tan 25°

h / tan 25° = x

h / (x + 350) = tan 12°

h = (x + 350) tan 12°

h = x tan 12° + 350 tan 12°

h - 350 tan 12° = x tan 12°

(h - 350 tan 12°) / tan 12° = x

(h - 350 tan 12°) / tan 12° = h / tan 25°

Can you sole for h and answer?