An observer 80 ft above the surface of the water measures an angle of depression of 0.7o to a distant ship. How many miles is the ship from the base of the lighthouse? (5280 ft = 1 mile)

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Mathematics

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4 November, 08:34

An observer 80 ft above the surface of the water measures an angle of depression of 0.7o to a distant ship. How many miles is the ship from the base of the lighthouse? (5280 ft = 1 mile)

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Ava Branch · Answer 1

1.24 miles

Step-by-step explanation:

If the angle of depression is 0.7 degrees, we can use the tangent of the angle to find the relation between the distance from the lighthouse to the ship and the observer's elevation.

tangent (0.7) = observer's elevation / distance from the lighthouse to the ship

0.012218 = 80 / D

D = 80/0.012218 = 6547.72 feet

Now, converting from feet to miles, we have:

D = 6547.72/5280 = 1.24 miles