What is the height of the mountain, relative to its base?

Question

The length of the slope of a mountain is 2740 m, and it makes an angle of 12.4° with the horizontal. What is the height of the mountain, relative to its base?

Answer 1

Hi James,

This is just a little trigonometry.

1. Draw a right triangle where the slope of the mountain is the hypotenuse
2. 12.4^o is the angle between the hypotenuse and the ground
3. So the height that you're looking for is the opposite side from that angle.
4. Since you know the angle, and 1 side, you can use a trig expression to find the height.
5. sin = opp/ hyp
6. Check: Your answer should be much lower than the length of the slope. It's probably only a few hundred meters tall relative to the base.