Question

1. Given right triangle ABC with the right angle C and sin A = 1/3, which is of the following expression is also equal to 1/3?

A. cos B
B. cos(90° - A)
C. sin(90°- B)
D. Both A and B

2. The maximum slope for a hand propelled wheel chair ramp should be a 1-inch rise to every 12 inch of length. What is that maximum ramp angle recommended to the nearest degree?

Answer 1

1) B

2) About 5°.

Explanation:

1)

We can use the following co-function identity:

`\sin(\theta)=\cos(90-\theta)`

Substitute A for θ:

`\sin(A)=\cos(90-A)`

Since we know that sin(A) is 1/3, this means that cos(90-A) must also be 1/3.

So, our answer is B.

2)

Refer to the drawing.

Remember that 1-inch rise is a height of 1 while a 12 inch length is a length of 12.

So, to find the maximum ramp angle, we simply need to find the value of x.

We know the sides opposite and adjacent to x. So, we can use tangent:

`\tan(x)=\text{opp}/\text{adj}`

Substitute 1 for the opposite side and 12 for the adjacent side:

`\tan(x)=1/12`

Take the inverse tangent of both sides:

`x=\tan^(-1)(1/12)`

Use a calculator. Make sure you're in Degrees mode:

`x\approx4.76\textdegree\approx5\textdegree`

So, the maximum ramp angle should be about 5°