the ski lift chair at a ski report is 2560m long. on average, the ski lift rises 15.2 degree above the horizontal. how high is the top of the ski lift relative to the base?
draw a diagram.
h/2560 = sin 15.2°
h = 2560*.2622
h = 671
To find the height of the top of the ski lift relative to the base, we can use basic trigonometry. Here's how you can calculate it:
1. Identify the given values:
- Length of the ski lift chair: 2560 m
- Angle of elevation: 15.2 degrees
2. Draw a diagram:
- Draw a straight horizontal line to represent the base of the ski lift.
- From the starting point on the base, draw a line at an angle of 15.2 degrees above the horizontal. This line represents the path of the ski lift.
3. Identify the trigonometric relationship:
- In this case, we want to find the vertical height of the ski lift, which is the opposite side (opposite the angle of elevation) in a right-angled triangle.
4. Apply the trigonometric relationship:
- In a right-angled triangle, the trigonometric relationship for the sine of an angle is:
sin(angle) = opposite/hypotenuse
- Rearrange the formula to solve for the height (opposite):
opposite = sin(angle) * hypotenuse
5. Plug in the values and calculate:
- substitute the given values into the formula:
opposite = sin(15.2) * 2560
- Calculate the height:
opposite ≈ 0.2624 * 2560
opposite ≈ 672.26 meters
Therefore, the top of the ski lift is approximately 672.26 meters higher than the base.