To solve this problem, we can use trigonometry.
Let's label the distance from the lighthouse to the patrol boat as "x" and the distance from the lighthouse to the capsized boat as "y".
From the given information, we can apply the tangent function to find the distances.
For the patrol boat:
tan(9°) = x/90
x = 90 * tan(9°)
x ≈ 14.99 meters
For the capsized boat:
tan(12.5°) = y/90
y = 90 * tan(12.5°)
y ≈ 19.65 meters
To find the distance between the two boats, we can subtract the distances from the lighthouse to each boat.
Distance between the two boats = y - x
Distance between the two boats ≈ 19.65 - 14.99
Distance between the two boats ≈ 4.66 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°.
How far from the lighthouse is the patrol boat?
How far from the lighthouse is the capsized boat?
If the two boats are on the opposite side of the lighthouse, how far apart are the two boats?
1 answer
1 answer