Answer These Three Questions

Question

1a. Complete the following table (use a calculator):

x	sin(x)	cos(x)	[sin(x)]2 + [cos(x)]2
25º
40º
65º
75º
90º

1b. Describe the pattern that you see in the table for the right column.

 

2. A wheelchair ramp must form an angle no greater than 4.8 degrees with the ground. If a 1.8 foot high ramp is needed, what is the minimum horizontal length for the ramp so it satisfies the angle requirement? Include a sketch of the ramp.



3. Solve the triangle below without using either the cosine or tangent ratios. Show your work.

1. 

Answer 1

1) Just use your calculator as the problem requests. For 1b), the pattern in column 3 will be obvious once you fill it in.

2) Draw a triangle. tangent(4.8°) = opposite/adjacent = 1.8/adjacent. Solve for adjacent which is the horizontal distance.

3) Sin(23°) = opposite/hypotenuse = a/16, so sin(23°) · 16 = a. Use your calculator to get the answer.

Cos(23°) = adjacent/hypotenuse = b/16, so cos(23°) · 16 = b. Use your calculator to get the answer.