Question

Janine walks on a circular track whose radius is 60 meters. If she walks a total of 100 meters, which of the following represents the radian angle she rotates about the center of the track?
(1) 5/3
(2) 3/5
(3) 5π/3
(4) 3π/5

Answer 1

Answer: OPTION 1

Step-by-step explanation:

For this exercise you need to remember that, by definition, the Arc length can be calculated with the following formula:

$arc\ length=rC$

where "C" is the central angle of the arc in radians and "r" is the radius.

Since you need to find the Central  angle, you have to solve for "C" from that formula, as following:

$C=\frac{arc\ length}{r}$

According to the information given in the exercise, you can identify that:

$arc\ length=100\ m\\\\r=60\ m$

Therefore, the final step is to substitute these values into the formula and evaluate, in order to find the value of "C":

$C=\frac{100\ m}{60\ m} \\\\C=\frac{5}{3}\ rad$