Question

A dog that has been tethered with a 20-foot lead makes the path shown here. If the length of the path is 45 feet, the measure of the angle theta is ? radians. (Image Below)

Answer 1

We have our relationship between arc length, radial length, and anangle theta:
\(\large\rm s=r\cdot\theta\)

Our unknown in this case is theta. This is what we want to solve for.
Let's isolate theta by dividing by the radial length r,
\[\large\rm \frac{s}{r}=\theta\]And plug in the information they gave us,\[\large\rm \frac{45}{20}=\theta\]

Answer 2

Just simplify your answer your from there.