a ski slope on a mountain has an angle of elevation of 25.2 degrees. the vertical height of the slope is 1808 feet. how long is the slope?
I would draw a right-angled triangle, marking the "vertical height" with 1808, and the base angle as 25.2º
does the trig ratio opposite/hypotenuse ring a bell?
To find the length of the slope, we can use the trigonometric function tangent.
Tangent(angle) = Opposite/Adjacent
In this case, the angle of elevation is 25.2 degrees, and the vertical height (opposite side) is 1808 feet. We need to find the length of the slope (adjacent side).
So, we have:
Tangent(25.2°) = 1808/x
First, let's take the tangent of 25.2 degrees:
tan(25.2°) ≈ 0.4685
Now, substitute this value into our equation:
0.4685 = 1808/x
To solve for x, cross multiply:
0.4685 * x = 1808
Divide both sides by 0.4685:
x = 1808 / 0.4685
x ≈ 3861.93
Therefore, the length of the slope is approximately 3861.93 feet.
To find the length of the slope, we can use the trigonometric function known as tangent. Tangent (tan) of an angle is the ratio of the opposite side to the adjacent side of a right triangle. In this case, the opposite side is the vertical height of the slope (1808 feet), and the angle of elevation is 25.2 degrees.
So, we can use the formula:
tan(angle) = opposite / adjacent
Plugging in the values:
tan(25.2°) = 1808 / adjacent
To solve for the adjacent side (length of the slope):
1. Take the tangent of 25.2 degrees: tan(25.2°) ≈ 0.4663
2. Divide the opposite side by the tangent: 1808 / 0.4663 ≈ 3875.5
Therefore, the length of the slope is approximately 3875.5 feet.