Math Help Trigonometry

Question

The recommended angle for a wheel chair ramp is 5 degrees. If the rise of the ramp to go up the steps is 6 feet, find the horizontal run length that the ramp must start. 

Answer 1

The rise of the ramp (6 feet) is the side of a right triangle opposite the 5 degree angle, the horizontal run length (call it x) is the side adjacent to the 5 degree angle. So, since tangent of an angle is opposite / adjacent, we have the equation tan(5 degrees) = 6 / x

Finding tan(5 degrees) = .0875 on a calculator, this equation becomes

.0875 = 6 / x

Multiply both sides by x to get x out of the denominator gives

.0875 x = 6

Divide by .0875 gives

x = 6 / .0875

So x = 68.6 feet