From the top of a 200-ft lighthouse, the angle of depression to a ship in the ocean is 23 degrees. How far is the ship from the base of the lighthouse?
Greg !
Enough of "homework - dumping"
Show some work before any more help is given.
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To find the distance from the base of the lighthouse to the ship, we can use trigonometry. In this case, we have the angle of depression, which is the angle between the horizontal line and the line of sight from the top of the lighthouse to the ship.
Let's denote the distance from the base of the lighthouse to the ship as 'x'.
Using trigonometry, we can determine that the tangent of the angle of depression is equal to the opposite side (200 ft, the height of the lighthouse) divided by the adjacent side (the distance from the base of the lighthouse to the ship, 'x').
So we have:
tan(23 degrees) = 200 ft / x
To find 'x', we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by 'x':
x * tan(23 degrees) = 200 ft
Now, divide both sides of the equation by tan(23 degrees):
x = 200 ft / tan(23 degrees)
Using a calculator, we can find the value of tan(23 degrees) to be approximately 0.4245.
Now, substitute this value back into the equation:
x = 200 ft / 0.4245
Calculating this expression, we find:
x ≈ 471.24 ft
Therefore, the ship is approximately 471.24 feet away from the base of the lighthouse.