From the top of a cliff 50 m high the angle of depression to a boat is 30 degrees. Determine the distance between boat and foot of the cliff.

To solve this problem, we can use the tangent of the angle of depression, which is the ratio of the opposite side (height of the cliff) to the adjacent side (distance between the boat and the foot of the cliff).

Step 1: Identify the given information. The height of the cliff (opposite side) is 50 m and the angle of depression is 30 degrees.

Step 2: Set up the equation using the tangent of the angle of depression. In this case, tan(30) = height / distance.

Step 3: Substitute the given information into the equation. tan(30) = 50 / distance.

Step 4: Solve the equation for the distance. The distance = 50 / tan(30).

Step 5: Calculate the distance. The distance is approximately 86.60 m.

So, the distance between the boat and the foot of the cliff is approximately 86.60 m.