Question

CAN SOMEONE PLEASE PLEASE HELP ME ON THIS IM DESPERATE

Answer 1

Answer:

The angle has a measure of $\frac{5\pi}{6}$ radians.

Step-by-step explanation:

According to the statement, an angle centered at the center of the circle covers an arc of $\frac{25\pi}{6}$ units, the arc is a portion of the circunference. We include a figure representing the circle below.

Where:

$R$ - Radius, measured in units.

$s$ - Arc, measured in units.

$\alpha$ - Angle of the arc, measured in radians.

From Geometry, we can calculate the length of the arc by means of this equation:

$s = \alpha\cdot R$ (1)

If we know that $R = 5$ and $s = \frac{25\pi}{6}$, then the angle of the arc is:

$\alpha = \frac{s}{R}$

$\alpha = \frac{\frac{25\pi}{6} }{5}$

$\alpha = \frac{25\pi}{30}$

$\alpha = \frac{5\pi}{6}\,rad$

The angle has a measure of $\frac{5\pi}{6}$ radians.