a ship with a bearing of 33 degrees first light a lighthouse at a bearing of north 65 degrees east.after travelling 8.5 miles, the ship observed the lighthouse at bearing of south 50 degrees east. find the distance from the ship to the lighthouse when the first sighting was made?

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29-07-2022
Mathematics

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a ship with a bearing of 33 degrees first light a lighthouse at a bearing of north 65 degrees east.after travelling 8.5 miles, the ship observed the lighthouse at bearing of south 50 degrees east. find the distance from the ship to the lighthouse when the first sighting was made?

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akposevictor akposevictor · Answer 1 · 2022-08-01T22:08:59+02:00

Applying the law of sines, when the first lighting was made, the distance from the ship to the lighthouse was: 3.2 miles.

What is the Law of Sines?

The law of sines is expressed by the equation, sin A/a = sin B/b = sin C/c.

Using the information we are provided with, the diagram that shows the ship and other information is drawn and shown in the image attached below, where:

m∠CAB = 65 + 30 = 95°

m∠BCA = 50 - 30 = 20°

m∠B = 180 - 95 - 20 = 65°

c = the distance from the ship to the lighthouse

Considering triangle ABC, use the Law of Sines to find c:

sin B/b = sin C/c

B = 65°

b = 8.5 miles

C = 20°

Plug in the values

sin 65/8.5 = sin 20/c

Cross multiply

c(sin 65) = (8.5 × sin 200)

Divide both sides by sin 65

c(sin 65)/sin 65 = (8.5 × sin 200)/sin 65

c = (8.5 × sin 200)/sin 65

c ≈ 3.2 miles

Thus, when the first lighting was made, the distance from the ship to the lighthouse was: 3.2 miles.

Learn more about the law of sines on:

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