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?........ Do I use cos, tan, or sin? I did the rest of the worksheet but I'm not sure for this one

To solve this problem, you will use the trigonometric function tangent (tan). The tangent of an angle of elevation is defined as the ratio of the opposite side to the adjacent side.

Let's label the sides of the triangle formed by Casey, the lighthouse, and the ground:
- The height of the lighthouse is the opposite side (O), which is 84 feet.
- Casey's height is the adjacent side (A), which is 6 feet.
- The distance between Casey and the base of the lighthouse is the hypotenuse (H), which we want to find.

Now, we can set up the tangent function:

tan(angle) = opposite / adjacent

tan(58 degrees) = 84 / 6

Next, let's solve for the angle's tangent:

tan(58 degrees) ≈ 1.747

Now, we can rearrange the formula to solve for the hypotenuse:

H = opposite / tan(angle)

H = 84 / 1.747

H ≈ 48.07 feet

Therefore, Casey is standing approximately 48.07 feet from the base of the lighthouse.