The angle of depression of a cliff is 58[deggree] if the cliff is 10.5m high,how far is the boat from the from the foot of the cliff
10.5 m * tan(90º - 58º) = d
To find the distance of the boat from the foot of the cliff, we can use the trigonometric concept of tangent.
Let's assume that the boat is at point B (bottom of the cliff), and the top of the cliff is at point C. We are given that the angle of depression (angle BCA) is 58 degrees, and the height of the cliff (BC) is 10.5m.
In a right triangle ABC, the tangent of an angle (in this case, angle BCA) is defined as the opposite side (BC) divided by the adjacent side (AB).
Therefore, we can use the tangent function to find the distance AB.
Tangent(58 degrees) = opposite/adjacent
Tan(58) = BC/AB
Tan(58) = 10.5/AB
Now, we can rearrange the equation to solve for AB:
AB = 10.5 / Tan(58)
Using a calculator, we can evaluate the right side of the equation:
AB ≈ 10.5 / 1.601
AB ≈ 6.559 meters
Therefore, the boat is approximately 6.559 meters away from the foot of the cliff.
To find the distance from the boat to the foot of the cliff, we can use trigonometry.
Let's assume that the boat is directly in front of the cliff.
We have the height of the cliff (10.5m) and the angle of depression (58 degrees).
The angle of depression is the angle formed between the horizontal line and the line of sight from the boat to the foot of the cliff.
We can use the tangent function to find the distance.
Tangent of the angle of depression = Opposite side / Adjacent side
In this case, the opposite side is the height of the cliff (10.5m) and the adjacent side is the distance we want to find.
So, we can write:
tan(58 degrees) = 10.5m / x
To solve for x, we can rearrange the equation:
x = 10.5m / tan(58 degrees)
Using a scientific calculator, we can find:
x ≈ 7.56m
Therefore, the boat is approximately 7.56 meters away from the foot of the cliff.