Find the degree measure of the central angle whose intercepted arc measures 8cm in a circle of radius 15cm.
Answer: -401.07 degrees
-401.07 degrees is the same as -41.07 degrees. That would be in the fourth quadrant. There should have been a figure associated with this problem showing the direction and place that the arc was located.
Let's just consider the size of the subtended angle.
An 8 cm arc on a 15 cm radius is 8/15 radian or
(8/15)(180/pi) = 96/pi = 30.56 degrees
I have no idea how you or your textbook came up with -401.07 degrees
To find the degree measure of a central angle, you need to use the formula:
Degree measure = (Intercepted arc length / Circumference) * 360 degrees
In this case, the intercepted arc measures 8cm, and the radius of the circle is 15cm. To find the circumference of the circle, you can use the formula:
Circumference = 2 * π * radius
Substituting the given radius, we get:
Circumference = 2 * π * 15 cm
Circumference = 30π cm
Now, we can substitute the values into the first formula:
Degree measure = (8 cm / 30π cm) * 360 degrees
Degree measure ≈ (0.2667 * 360) degrees
Degree measure ≈ 96 degrees
Therefore, the degree measure of the central angle whose intercepted arc measures 8cm in a circle of radius 15cm is approximately 96 degrees. It seems there was an error in the given answer (-401.07 degrees), as it does not match the calculations.