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

Answers ( )

    0
    2021-09-17T14:29:37+00:00

    Answer:

    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

    a: adjacent

    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

    0
    2021-09-17T14:29:51+00:00

    Answer:

    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

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