AB is a vertical cliff. C is a point 380m from the cliff. the angle of elevation to the top of the cliff is 58 degrees. calculate the height of the cliff
tan 58 = h/380
To calculate the height of the cliff, we can use trigonometric functions. In this case, we can use the tangent function because we have the opposite side (height of the cliff) and the adjacent side (distance from point C to the cliff) in relation to the angle of elevation.
The tangent function is defined as the ratio of the opposite side to the adjacent side of a right triangle.
Let's denote the height of the cliff as "h". Using the given information, we have:
Opposite side (height of the cliff) = h
Adjacent side (distance from point C to the cliff) = 380m
Angle of elevation = 58 degrees
Using the tangent function:
tan(angle) = opposite/adjacent
tan(58) = h/380
Now, we can solve for "h":
h = tan(58) * 380
Using a calculator, we find:
h ≈ 520.28 meters
Thus, the height of the cliff is approximately 520.28 meters.