from the top of a 250 ft lighthouse the angle of depression to a ship in the ocean is 18 degrees. how far is the ship from the base of the light house?

did you make a diagram?

tan 72° = x/250
x = 250tan 72°
= ....

769.421

To find the distance from the ship to the base of the lighthouse, we can use trigonometry and the tangent function.

Let's label the distance from the base of the lighthouse to the ship as "x".

The angle of depression is the angle formed between the horizontal line from the top of the lighthouse to the ship and the line of sight from the top of the lighthouse to the ship.

We can use the tangent function to relate the angle of depression to the ratio of the opposite side (250 ft) to the adjacent side (x):

tan(18°) = opposite/adjacent
tan(18°) = 250/x

To solve for x, we can rearrange the equation:

x = 250 / tan(18°)

Using a calculator, we can find the value of the tangent of 18 degrees and calculate the distance from the ship to the base of the lighthouse:

x ≈ 250 / 0.3249
x ≈ 769.2 ft

Therefore, the ship is approximately 769.2 ft away from the base of the lighthouse.

To find the distance from the base of the lighthouse to the ship, we can use trigonometry. In this case, we can use the tangent function because we have the opposite and adjacent sides of the right triangle.

Let's define the variables:
- H: Height of the lighthouse (250 ft)
- θ: Angle of depression (18 degrees)
- x: Distance from the base of the lighthouse to the ship (unknown)

Using the tangent function:
tan(θ) = Opposite / Adjacent

The opposite side is the height of the lighthouse, and the adjacent side is the distance from the base of the lighthouse to the ship.

Therefore, we can set up the equation:
tan(18°) = H / x

Substituting the known values:
tan(18°) = 250 / x

Now, we need to solve this equation to find the value of x.

Step 1: Plug the equation into a calculator or use the tangent of 18 degrees (approximately 0.3249).
0.3249 = 250 / x

Step 2: Solve for x by isolating it on one side of the equation.
Multiply both sides of the equation by x:
0.3249x = 250

Step 3: Divide both sides of the equation by 0.3249 to solve for x.
x = 250 / 0.3249

Calculating this value, we find that x is approximately 770.33 feet.

Therefore, the ship is approximately 770.33 feet from the base of the lighthouse.