Problem

Circle $O$ shown below has a radius of 10 inches. Find, to the nearest tenth of a degree, the measure of the angle, $x$, that forms an arc whose length is 26 inches.

Solution

Step 1 :Given a circle with radius 10 inches and an arc length of 26 inches, we can use the formula for arc length: Arc length = radius * angle (in radians)

Step 2 :Convert the angle from radians to degrees using the conversion factor: 1 radian = 180 degrees / pi

Step 3 :Set up the equation: 26 = 10 * x (in radians)

Step 4 :Convert x to degrees and solve for x: \( x = \frac{26}{10} \cdot \frac{180}{\pi} \)

Step 5 :Calculate x: \( x \approx 149.0 \)

Step 6 :The measure of angle x, to the nearest tenth of a degree, is \( \boxed{149.0} \) degrees

From Solvely APP
Source: https://solvelyapp.com/problems/8765/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download