Question

A man standing on top of a cliff 90m high is in line with two buoys whose angle of depression are 15 degrees and 19 degrees respectively. Calculate the distance between the buoys to one decimal place.

Answer 1

To calculate the distance between two buoys from a cliff using angles of depression, apply trigonometric ratios to find the horizontal distances and subtract one from the other.

Step-by-step explanation:

The subject question involves using trigonometry to calculate the distance between two buoys observed at different angles of depression from the top of a cliff. We're given a cliff height of 90 meters and depression angles of 15 degrees and 19 degrees, respectively. By applying trigonometric ratios (specifically, the tangent ratio), we can find the horizontal distances from the man to each buoy. Then, the difference between these two distances will give us the distance between the two buoys.

1. Calculate the horizontal distance to the first buoy using the tangent of 15 degrees: distance = 90m / tan(15°).
2. Calculate the horizontal distance to the second buoy using the tangent of 19 degrees: distance = 90m / tan(19°).
3. Subtract the smaller distance from the larger distance to find the distance between the buoys.

By resolving the calculation to one decimal place, we will have the desired result, which is the distance between the buoys.