## From the top of a 150-ft lighthouse, the angle of depression to a ship in the ocean is 22°. How far is the ship from the base of the lightho

Question

From the top of a 150-ft lighthouse, the angle of depression to a ship in the ocean is 22°. How far is the ship from the base of the lighthouse? (Round your answer to the nearest foot.)

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1 month 2021-09-17T14:28:07+00:00 2 Answers 0

the ship is at a distance of 60 feet

Step-by-step explanation:

we have to think of the problem as a right triangle, since

we have 2 legs and 1 hypotenuse, we know the measure of the leg that gives us the height and the angle that that leg touches

the leg we want to calculate is the opposite of the angle we have, since it does not touch

well to start we have to know the relationship between angles, legs and the hypotenuse

o: opposite

h: hypotenuse

sin α = o/h

cos α= a/h

tan α = o/a

we see that it has (angle, adjacent, opposite)

is the tangent

tan α = o/a

tan 22 = o/150

tan 22 * 150 = o

60.6ft = o

round to the nearest foot

60ft

the ship is at a distance of 60 feet

Step-by-step explanation:

Considering the situation, a right angle triangle is formed. The height of the lighthouse represents the opposite side of the right angle triangle.

The horizontal distance, h between the ship and the base of the lighthouse represents the adjacent side of the right angle triangle.

If the angle of depression to the fire that is 22°, the angle of elevation of the lighthouse from the ship is also 7° because they are alternate angles.

To determine h, we would apply

the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan 22 = 150/h

h = 150/tan22 = 150/0.4040

h = 371 feet