The angle of depression From the top of a 75-foot lighthouse to a ship out in the ocean is 40'. How far is the ship From the lighthous?
To determine the distance of the ship from the lighthouse, we can use trigonometry and the given angle of depression.
Let's label the distance from the lighthouse to the ship as "d". The angle of depression, which is the angle formed by looking downward from a line parallel to the horizon, is given as 40 degrees.
We can use the tangent function to find the distance:
tan(angle of depression) = opposite/adjacent
In this case, the opposite side is the height of the lighthouse, which is 75 feet. The adjacent side represents the distance from the lighthouse to the ship, which we want to determine (d).
Now we can set up the equation:
tan(40 degrees) = 75 feet / d
To solve for d, we can rearrange the equation:
d = 75 feet / tan(40 degrees)
Using a calculator, we can find the tangent of 40 degrees:
tan(40 degrees) ≈ 0.8391
Now, substitute this value into the equation:
d ≈ 75 feet / 0.8391
By dividing 75 feet by 0.8391, we can calculate the approximate distance from the lighthouse to the ship:
d ≈ 89.36 feet
Therefore, the ship is approximately 89.36 feet away from the lighthouse.
75/x = tan 40°
I assume you meant 40°, not 40', as that would have
(a) been hard to measure
(b) put the ship well over the horizon