Question

For problems 1-3, use the information in the diagram to find the angle measure of in radians. Round your answer to the nearest ten-thousandth, if necessary.

Answer 1

1. 4.25 radians
2. 2.4 radians
3. 0.625 radians

Explanation:

You want the angles associated with different arc lengths and radii.

Angle

The length of an arc is given by the formula ...

s = rθ . . . . . θ is the angle in radians, r is the radius

Solving for θ gives ...

θ = s/r

1.

For s=17 in, r=4 in, ...

θ = (17 in)/(4 in) = 4.25 . . . . radians

2.

For s=12 ft, r=5 ft, ...

θ = (12 ft)/(5 ft) = 2.4 . . . . radians

3.

For s=8.5 mm, r = 13.6 mm, ...

θ = (8.5 mm)/(13.6 mm) = 0.625 . . . . radians