Explanation:
let's assume the numbers are correct, and the lighthouse light is really 4000 ft high.
so we have a right-angled triangle.
the ground distance boat to lighthouse = 2500 ft.
the height of the lighthouse light = 4000 ft.
the line of sight boat to lighthouse light.
we know the angle at the lighthouse bottom : 90°.
the line of sight is the Hypotenuse of the triangle
line of sight² = 2500² + 4000² = 6,250,000 + 16,000,000 =
= 22,250,000
line of sight = 4,716.990566... ft
we can use the law of sine to solve the question.
a/sin(A) = b/sin(B) = c/sin(C)
with the sides and the correlated angles being always opposite.
we have here
line of sight/sin(90) = 4000/sin(angle at boat)
sin(angle at boat) = 4000×sin(90)/line of sight =
= 0.847998304...
angle at the boat = 57.99461679...° ≈ 58°