The angle of depressionof a boy from a point on a lighthouse 30.5 meters above the surface of the water is 3°
3? i didn't realize that would be it. Thanks for answering my question!
To find the distance of the boy from the lighthouse, we can use trigonometry. The angle of depression represents the angle between the line of sight from the lighthouse to the boy and a horizontal line. In this case, the opposite side is the height of the lighthouse above the water level (30.5 meters), and the angle is 3 degrees.
We can use the tangent function (tan) to find the distance (d) of the boy from the lighthouse:
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the lighthouse above the water level (30.5 meters), and we need to find the adjacent side, which is the distance from the lighthouse to the boy (d). Rearranging the equation, we have:
d = opposite / tan(angle)
Plugging in the values:
d = 30.5 meters / tan(3°)
Using a calculator, we can find the tangent of 3 degrees:
tan(3°) ≈ 0.0524
Now, we can calculate the distance:
d ≈ 30.5 meters / 0.0524
d ≈ 583.97 meters
Therefore, the boy is approximately 583.97 meters away from the lighthouse.