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A boat is located 2500 ft from the base of a lighthouse. A passenger on the boat can see the top of the lighthouse 4000 ft high. What is the angle from the passenger to the top of the lighthouse?​

User Taseenb
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1 Answer

9 votes

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°

User Tamarisk
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