Let's assume that they are in the same line of sight, that is, the two ships and the lighthouse are in the same plane.
Label the farther ship A and the nearer ship B
Label the top of the lighthouse L and its bottom M
I see the following angles,
angle A = 20°
angle LBM =34° and AB=90 ft
in triangle LAB
angle A= 20
angle ABL = 180-34 = 146° which makes
angle ALB = 14°
by the Sine Law:
LB/sin20 = 90/sin14
LB = 90sin20/sin14
In the right-angled triangle LBM,
BM/LB= cos34
BM = LBcos34
= (90sin20/sin14)(cos34)
= ....
only now would I go to my calculator
Many people would do this using tangents or cotangents, but I always think that way is harder to understand.
A child on top of a lighthouse observes two ships that are 90 ft apart from each other. The angles of the depression of the two ships are 34º and 20º. How far is the closest ship from the base of the lighthouse?
I'm sorry, I would show my work, I just don't know if I could put a picture on here.
1 answer
1 answer