Question

Jen is on the platform of her boat. She sights the top of a lighthouse at an angle of 30º as shown below. She knows that the height of the lighthouse is 50 meters.

How far is Jen from the base of the lighthouse, in meters?

Answer 1

To find the distance Jen is from the base of the lighthouse, we can use trigonometry. We can use the tangent function to calculate the distance.

Step-by-step explanation:

To find the distance Jen is from the base of the lighthouse, we can use trigonometry. We can use the tangent function to calculate the distance. The tangent of an angle is equal to the opposite side divided by the adjacent side of a right triangle.

In this case, the adjacent side is the distance from Jen to the base of the lighthouse and the opposite side is the height of the lighthouse. So, we can set up the following equation:

Tan(30 degrees) = Opposite/Adjacent

Tan(30 degrees) = 50/Adjacent

Using a calculator, we can find that the tangent of 30 degrees is approximately 0.577. So, we can rewrite the equation as:

0.577 = 50/Adjacent

Now, we can solve for the adjacent side by multiplying both sides of the equation by the adjacent side:

Adjacent = 50 / 0.577

Using a calculator, we find that the adjacent side is approximately 86.781 meters.