boy walks 58 feet up a ramp having a 22.5° inclination. How high is he standing from the ground?

Answer 1

58sin22.5 = about 22.2 =how high up he is. sine is opposite side over hypotenuse. 58 is the hypotenuse, so h x o/h = o = how high up he is

o = hsin22.5 = 58sin22.5 = 58(.38258) = 22.5 feet high. (it's sort of a coincidence that the height and angle have the same numerical value.

use a calculator for sin22.5 or use the half angle formula

sin(x/2) = sqr((1-cosx)/2) as you may know cos45 = sqr2/2 = about 1.414/2 = 0.707

the 45 degree right triangle is so common, many people just know the sin45=cos45=sqr2/2

sin(22.5) = sin(45/2) = sqr((1-0.707)/2) = sqr(.293/2) = sqr(.1465) = about 0.38

Answer 2

For this type of problem you should always draw a picture and find the right triangle. Then you can see that:

sin(22.5°) = height/ramp

sin(22.5°) = height/58

Solve for height.