From the top of a lighthouse 210 feet high, the angle if depression to a boat is 27 degress. Find the distance from the boat to the food of the lighthouse. The lighthouse was built at sea level.
To find the distance from the boat to the foot of the lighthouse, you can use trigonometry. In this case, we can use the tangent function.
The angle of depression is the angle between the line from the top of the lighthouse to the boat and the horizontal line. In this case, the angle of depression is 27 degrees.
Let's assume that the distance from the boat to the foot of the lighthouse is represented by "x".
We know that the height of the lighthouse is 210 feet, and the angle of depression is 27 degrees. Using the tangent function, we can set up the following equation:
tan(27°) = (height of the lighthouse) / (distance from boat to foot of the lighthouse)
tan(27°) = 210 / x
Now, we can solve for x by rearranging the equation:
x = 210 / tan(27°)
To find the value of x, you can use a scientific calculator or an online trigonometry calculator. By plugging in the values and solving, we find that x is approximately 467.7 feet.
Therefore, the distance from the boat to the foot of the lighthouse is approximately 467.7 feet.