Explanation:
we have a right-angled triangle here.
there is the ground distance boat to lighthouse.
there is the height of the lighthouse = 141 ft.
and there is the line of sight boat to lighthouse light.
the angle at the boat is 12°.
the angle at the lighthouse bottom is 90°.
therefore, the angle at the lighthouse light is 180 - 90 - 12 = 78°
we use the law of sine to solve this.
a/sin(A) = b/sin(B) = c/sin(C)
with the sides and correlated angles being always opposite.
so, we have here
141/sin(12) = ground distance/sin(78)
ground distance = 141×sin(78)/sin(12) = 663.3528454... ft
≈ 663.35 ft