Type the correct answer in the box. Use numerals instead of words. In the image below, point J is located at the center of the circle, and s is the length of the arc located inside of the triangle. Given that m∠JKL = 94°, m∠KLJ = 41°, and the radius of the circle is 10 units, find s, rounded to the nearest hundredth. s = ___ units

To find the length of arc \( s \) inside of triangle JKL, where \( J \) is the center of the circle, we first need to find the measure of the third angle of the triangle, \( m∠JLK \), and then use that measure to calculate the length of the arc.

The sum of the angles in any triangle is 180°. We are given that \( m∠JKL = 94° \) and \( m∠KLJ = 41° \). Now we calculate the third angle as follows:

\( m∠JLK = 180° - m∠JKL - m∠KLJ \) \( m∠JLK = 180° - 94° - 41° \) \( m∠JLK = 180° - 135° \) \( m∠JLK = 45° \)

Now that we know the measure of the third angle, which is also the angle at the center of the circle that subtends the arc \( s \), we can calculate the length of the arc. The circumference of the circle is the total distance around the circle, which is given by \( 2πr \) where \( r \) is the radius. The length of the arc \( s \) is a portion of the circumference and is proportional to the angle subtended by the arc over the total 360° in a circle.

The formula to calculate the length of an arc is \( s = 2πr \times (\frac{\text{angle in degrees}}{360°}) \). Plugging in the known values, we get:

\( s = 2π \times 10 \times (\frac{45°}{360°}) \) \( s = 20π \times (\frac{1}{8}) \) \( s = \frac{20π}{8} \) \( s = \frac{5π}{2} \)

For the final answer, let's calculate \( s \) and round it to the nearest hundredth, considering \( π ≈ 3.14159 \):

\( s ≈ \frac{5 \times 3.14159}{2} \) \( s ≈ \frac{15.70795}{2} \) \( s ≈ 7.853975 \)

Rounded to the nearest hundredth:

\( s ≈ 7.85 \) units

So, the arc length \( s \) is approximately 7.85 units.