the angle of elevation from bottom to the top of the mountain has a measure of 60 degrees. suppose a ski lift to the top is 2000 feet long. how high is the mountain to the nearest feet?
Am I suppose to find the sine of 60?
Yes. sin 60 = x/2000
Thank you.
You're welcome!
Yes, to find the height of the mountain, you can use the sine function. Let's use the given angle of elevation of 60 degrees. To find the height of the mountain, we need to find the length of the side opposite to the angle of elevation (the height) in the right-angled triangle formed by the mountain, the ski lift, and the horizontal ground.
In this case, the ski lift represents the hypotenuse of the triangle, and the height of the mountain is the opposite side to the angle of elevation. So, we can use the sine function, which relates the ratio of the opposite side to the hypotenuse.
The formula for calculating the height (opposite side) is:
Height = Hypotenuse * sin(angle)
Plugging in the values:
Height = 2000 feet * sin(60 degrees)
Now, you can calculate the height by finding the sine of 60 degrees.