A sled travels from point A at the top of a hill to Point B at the bottom. If the distance from point A to point B is 120 m and the vertical change is 50 m, find the angle of depression to the nearest degree.
the angle is x, where
sin x = 50/120
To find the angle of depression, we need to use trigonometry. The angle of depression is defined as the acute angle below the horizontal line of sight when looking down from an elevated point.
In this case, we have a right triangle formed by the vertical change of 50 m (opposite side), the distance of 120 m (hypotenuse), and the horizontal distance (adjacent side) between Points A and B.
To find the angle of depression, we will use the inverse tangent function (arctan). The formula for tangent is:
tan(angle) = opposite/adjacent
In our case, we know the opposite side (50 m) and the adjacent side is the distance between Points A and B (120 m). Substituting these values into the formula, we get:
tan(angle) = 50/120
Next, we need to find the inverse tangent (arctan) of both sides of the equation to isolate the angle:
angle = arctan(50/120)
Using a calculator, input the ratio 50/120 and find the arctan or inverse tangent. The result is approximately 22.62 degrees.
Therefore, the angle of depression, to the nearest degree, is 23 degrees.