Final answer:
The angle of depression of the boat from the top of the cliff is calculated using the tangent of the angle, which equals the height of the cliff divided by the distance from the foot of the cliff to the boat. This gives an angle of depression of approximately 15.0 degrees.
Step-by-step explanation:
To calculate the angle of depression of the boat from the top of the cliff which is 20m high, and with the boat situated 75m from the foot of the cliff, we use trigonometry. Specifically, we employ the tangent function, which is the ratio of the opposite side to the adjacent side of a right-angled triangle.
In this scenario, the height of the cliff represents the opposite side, and the distance from the foot of the cliff to the boat represents the adjacent side. Thus, we can use the following formula:
tangent(angle of depression) = opposite / adjacent
So inserting our values:
tangent(angle of depression) = 20 / 75
To solve for the angle of depression, we take the arctangent (inverse tangent) of the ratio:
angle of depression = arctangent(20 / 75)
Using a calculator, this gives us:
angle of depression ≈ arctangent(0.2667)
angle of depression ≈ 15.0 degrees
Therefore, the angle of depression of the boat from the top of the cliff is approximately 15.0 degrees.