To solve this problem, we can use trigonometry. Let's use the variable x to represent the distance between the lighthouse and the capsized boat, and y to represent the distance between the lighthouse and the patrol boat.
In the triangle formed by the lighthouse, the capsized boat, and the horizontal line, the angle of depression is 12.5°, and the opposite side is x. We can use tangent to relate these values:
tan(12.5°) = x/90
Rearranging the equation, we find:
x = 90 * tan(12.5°)
To find the distance between the lighthouse and the patrol boat, we can use the same logic. In the triangle formed by the lighthouse, the patrol boat, and the horizontal line, the angle of depression is 9°, and the opposite side is y.
tan(9°) = y/90
Rearranging the equation, we find:
y = 90 * tan(9°)
Now we can calculate the values of x and y.
x = 90 * tan(12.5°) ≈ 18.52 m
y = 90 * tan(9°) ≈ 14.69 m
Therefore, the distance between the lighthouse and the capsized boat is approximately 18.52 meters, and the distance between the lighthouse and the patrol boat is approximately 14.69 meters.
From the top of a 90 m lighthouse, an operator sees a capsized boat and determines an angle of depression of
12.5° to the boat. A patrol boat is also spotted at an angle of depression of 9°.
1 answer
1 answer