From the top of a 179-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?
distance=?
To find the distance between the ship and the base of the lighthouse, we can use trigonometry. Specifically, we can use the tangent function.
Let's call the distance from the base of the lighthouse to the ship "x". We can now set up a right triangle with the height of the lighthouse (179 ft) as the opposite side, and the distance from the base of the lighthouse to the ship (x) as the adjacent side. The angle of depression (22°) is the angle between the hypotenuse and the adjacent side.
Using the tangent function, we have:
tan(angle) = opposite/adjacent
tan(22°) = 179 ft / x
To find x, we can rearrange the equation:
x = 179 ft / tan(22°)
Now, let's calculate the distance from the base of the lighthouse to the ship:
x ≈ 482.38 ft
Therefore, the ship is approximately 482.38 ft away from the base of the lighthouse.
draw a picture to see the right triangle
tan(22º) = 179 ft / distance