From the top of a 300-ft lighthouse, the angle of depression to a ship in the ocean is 28°. How far is the ship from the base of the lighthouse? (Round your answer to the nearest foot.)
564 ft. Boom, answered my own question!!!!
To find the distance of the ship from the base of the lighthouse, we can use trigonometry.
The angle of depression is the angle between the horizontal line and the line from the top of the lighthouse to the ship. In this case, it is 28°.
Let's call the distance from the base of the lighthouse to the ship "x".
Using trigonometry, we can use the tangent function to find x:
tan(angle of depression) = opposite / adjacent
In this case, the opposite side is the height of the lighthouse which is 300 ft, and the adjacent side is the distance from the base of the lighthouse to the ship, which is x.
So, we have:
tan(28°) = 300 ft / x
To solve for x, we need to isolate it. We can do this by multiplying both sides of the equation by x:
x * tan(28°) = 300 ft
Now, divide both sides of the equation by tan(28°):
x = 300 ft / tan(28°)
Using a calculator, we can find the approximate value:
x ≈ 300 ft / tan(28°) ≈ 600 ft
Therefore, the ship is approximately 600 feet from the base of the lighthouse.
To find the distance between the ship and the base of the lighthouse, we can use trigonometry and the angle of depression.
Let's refer to the distance between the ship and the base of the lighthouse as "x." We have a right triangle formed by the lighthouse, the ship, and the distance "x."
In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the angle of depression of 28° is the angle between the lighthouse and the line connecting the lighthouse to the ship.
Therefore, we can use the tangent ratio to find the length of the opposite side (300 ft) and the adjacent side (x).
The tangent of the angle of depression is given by the formula:
tan(angle) = opposite/adjacent
tan(28°) = 300 ft / x
To find x, we rearrange the formula:
x = 300 ft / tan(28°)
Now, we can plug the values into a calculator to find the value of x:
x ≈ 624.95 ft
Rounding to the nearest foot, the ship is approximately 625 feet from the base of the lighthouse.