Ramp height - Math Central

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Quandaries & Queries

Question from Steve, a parent:

Hi there,
I need to find the height of a angle.
23 degree angle at 12 feet of length is how high from the ground?
Thank You
Steve

P.S. I don't remember this from high school! Why we need it. We are building a ramp that will tell us how flexable are 4x4 are. It is called an RTI ramp.

Hi Steve.

Is the length of 12 feet the horizontal length along the ground or the length of the ramp itself?

Assuming it is the length of the ramp itself, then the height would be 4.689 feet.

This is because the ramp is the hypotenuse in a right-angled triangle so the height h, the ramp length r, and the angle A are related by the equation h = r sin A. Since r is 12 and A is 23 degrees, h = 12 sin(23) = 4.689 feet.

That's about 4 foot, 8.25 inches.

Cheers,
Stephen La Rocque.

PS: If it is 12' along the ground rather than the ramp, then h = 12 tan (23) instead.

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