The captain of a ship at sea sights a lighthouse which is 280 feet tall.

The captain measures the the angle of elevation to the top of the lighthouse to be 25.

How far is the ship from the base of the lighthouse?

25=howfar*tan25

Now, I am wondering how he measured the angle of elevation at night....if you have ever been at sea at night, you know the problem: the surface and sky are both black, and you cannot see the horizon.

Casey sights the top of an 84 foot tall lighthouse at an angle of elevation of 58 degrees. If casey is 6 feet tall, how far is he standing from the base of the lighthouse?

To find the distance from the ship to the base of the lighthouse, we can use trigonometry. The angle of elevation and the height of the lighthouse form a right triangle, where the height of the lighthouse is the opposite side and the distance from the ship to the base is the adjacent side.

We can use the tangent function to calculate the distance. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case, we have the angle of elevation (25 degrees) and the height of the lighthouse (280 feet). Let's use the formula:

tan(angle) = height / distance

Plugging in the values:

tan(25) = 280 / distance

To find the distance, we can rearrange the formula:

distance = height / tan(angle)

Now we can compute the distance:

distance = 280 / tan(25) ≈ 660.29 feet

Therefore, the ship is approximately 660.29 feet away from the base of the lighthouse.

To find the distance between the ship and the base of the lighthouse, we can use trigonometry. Specifically, we can use the tangent function, which relates the angle of elevation and the relative lengths of the sides of a right triangle.

Let's label the distance between the ship and the base of the lighthouse as "x". We also know that the height of the lighthouse is 280 feet and the angle of elevation is 25 degrees.

The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the side opposite the angle of elevation is the height of the lighthouse, and the side adjacent to the angle is the distance between the ship and the base of the lighthouse (x).

Using the tangent function, we can write the following equation:

tan(25) = 280 / x

To find x, we can rearrange the equation:

x = 280 / tan(25)

Now, we can calculate the value of x using a scientific calculator. Dividing the height of the lighthouse (280) by the tangent of 25 degrees gives us the distance between the ship and the base of the lighthouse.