Law of sines problem. I think I got the answers 78.6229 and 101.3771 but I’m not sure if I interpreted the wording correctly.
+128407 We have a SSA-type problem
Let the lighthouse be located at C......angle ACB = 33°
C
36
A 20 B
We are looking for angle CBA
We can find angle CAB, first
Using the Law of Sines
sin ACB /20 = sinCAB / 36
sin (33) / 20 = sin(CAB) /36
(36/20)sin (33) = sinCAB
arcsin [ (36/20)sin(33)] = CAB ≈ 78.62°
Therefore a possible value for angle CBA ≈ 180 - 33 - 78.62 ≈ 68.38°
Another possible value for angle CAB = 180 - 78.62 ≈ 101.38°
Add this to the known angle ACB = 33 + 101.38 = 134.38°
Because this is < 180, we have two possible triangles
So....the other possible value for angle CBA = 180 - 134.38 = 45.62°
