Sitting in your sailboat, you see a lighthouse 500 feet away. Looking up at a 20°angle, you see the light at the top of the lighthouse. How far off the ground is the light in the lighthouse? Round your answer to the nearest tenth.
To solve this problem, we can use trigonometry. Let's break down the given information:
- The distance between the sailboat and the lighthouse is 500 feet.
- The angle at which you are looking up towards the light on top of the lighthouse is 20 degrees.
First, we need to find the height of the lighthouse. Let's label it as "h".
To find the height, we can use the tangent function:
tan(angle) = opposite/adjacent.
In this case, the opposite side is "h" (the height of the lighthouse) and the adjacent side is 500 feet (the distance between the sailboat and the lighthouse).
So, we have:
tan(20 degrees) = h/500.
To isolate "h", we can multiply both sides of the equation by 500:
500 * tan(20 degrees) = h.
Now, let's calculate the value of 500 * tan(20 degrees):
500 * tan(20 degrees) ≈ 180.773.
So, the approximate height of the light in the lighthouse is 180.8 feet.
500 tan20
Do the numbers.