Angle of Depression
Find the angle of depression from the top of the lighthouse 250 feet above water level to the water line of a ship 2.5 miles offshore.
1.085
tanθ = 250/(2.5*5280)
y’all dumb for this
To find the angle of depression, we need to use trigonometry. The angle of depression is the angle formed by a horizontal line and the line of sight from the observer (in this case, the top of the lighthouse) to the object (in this case, the water line of the ship).
First, let's convert the distance from miles to feet since the height of the lighthouse is given in feet. There are 5280 feet in a mile, so 2.5 miles is equal to 2.5 * 5280 = 13200 feet.
Now, let's label the given information on a diagram:
|
| . (lighthouse)
H | /
| /
| /
| / θ (angle of depression)
| /
| /
| /
| / __________________
|/____|__________________ (water line)
A 2.5 miles B
Here, H represents the height of the lighthouse (250 feet), and AB represents the distance from the lighthouse to the water line of the ship (13200 feet).
Let's use the tangent function to find the angle of depression:
tan(θ) = opposite/adjacent
In this case, the opposite side is the height of the lighthouse (H = 250 feet), and the adjacent side is the distance from the lighthouse to the water line of the ship (AB = 13200 feet).
Plugging in the values, we get:
tan(θ) = H/AB
tan(θ) = 250/13200
Now, let's find the value of θ:
θ = arctan(tan(θ))
θ = arctan(250/13200)
Using a calculator or an online tool, you can find that arctan(250/13200) is approximately 1.07 degrees.
Therefore, the angle of depression from the top of the lighthouse to the water line of the ship is approximately 1.07 degrees.