Daniel sees a lighthouse in the harbor. He estimates the angle of elevation is 60°. If the lighthouse is 120 feet tall, what is the approximate distance between Daniel and the top of the lighthouse? (Assume the lighthouse meets the ground at a right angle

To solve this problem, we can use trigonometry, specifically the sine function. The sine function relates the angle of elevation with the opposite side and the hypotenuse of a right triangle.

In this case, the opposite side is the height of the lighthouse (120 feet), and the angle of elevation is 60°. We can set up the equation as follows:

sin(60°) = opposite/hypotenuse

sin(60°) = 120 feet/hypotenuse

To isolate the hypotenuse, we can rearrange the equation:

hypotenuse = 120 feet / sin(60°)

Using a calculator or reference table, we find that sin(60°) is approximately 0.866. Substituting this value into the equation:

hypotenuse = 120 feet / 0.866

hypotenuse ≈ 138.53 feet

Therefore, the approximate distance between Daniel and the top of the lighthouse is approximately 138.53 feet.

To find the approximate distance between Daniel and the top of the lighthouse, we can use trigonometry. Specifically, we can use the tangent function.

Tangent function: tan(angle) = opposite/adjacent

In this case, the angle of elevation is 60° and the opposite side is the height of the lighthouse (120 feet). We want to find the adjacent side, which represents the distance between Daniel and the top of the lighthouse.

Rearranging the equation, we have:

adjacent = opposite / tan(angle)

Plugging in the values, we get:

adjacent = 120 / tan(60°)

Now, we need to calculate the tangent of 60°. In many scientific calculators, there's a "tan" button that can be used to find the tangent of an angle. If you don't have a calculator, you can use online trigonometric calculators or look up the tangent of 60° in a trigonometric table.

Using a calculator or table, we find that the tangent of 60° is approximately 1.732.

So, the calculation becomes:

adjacent = 120 / 1.732

Evaluating this division, we find that the approximate distance between Daniel and the top of the lighthouse is approximately 69.282 feet.

dude

tan 60 = 120/x;

x = 120/tan60