Circle O shown below has a radius of 26 inches. Find, to the nearest tenth of a degree, the measure of the angle, x, that forms an arc whose length is 44 inches. Answer:

Question

Circle  O shown below has a radius of 26 inches. Find, to the nearest tenth of  a degree, the measure of the angle,  x, that forms an arc whose length is 44 inches. Answer:

Bytelearn · Accepted Answer

Use Arc Length Formula: To find the measure of angle x that corresponds to an arc length of 44 inches on a circle with a radius of 26 inches, we can use the formula for arc length: $ arc \ length = r \times \theta $, where r is the radius and $ \theta $ is the angle in radians.Convert Radians to Degrees: First, we need to convert the angle from radians to degrees since the question asks for the answer in degrees. The conversion factor is $ \frac{180}{\pi} $ degrees per radian.Solve for Theta: We can rearrange the arc length formula to solve for $ \theta $ in radians: $ \theta = \frac{arc \ length}{r} $.Substitute Values: Substitute the given values into the formula: $ \theta = \frac{44 \ inches}{26 \ inches} $.Calculate Radians: Calculate the value of $ \theta $ in radians: $ \theta = \frac{44}{26} \approx 1.6923 $ radians.Convert to Degrees: Now convert $ \theta $ from radians to degrees: $ \theta \times \frac{180}{\pi} \approx 1.6923 \times \frac{180}{\pi} \approx 96.9231 $ degrees.Round to Nearest Tenth: Round the answer to the nearest tenth of a degree: $ \theta \approx 96.9 $ degrees.

Circle $O$ shown below has a radius of $26$ inches. Find, to the nearest tenth of $a$ degree, the measure of the angle, $x$ , that forms an arc whose length is $44$ inches. $\newline$ Answer: $\square^{\circ}$

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Circle $O$ shown below has a radius of $26$ inches. Find, to the nearest tenth of $a$ degree, the measure of the angle, $x$ , that forms an arc whose length is $44$ inches. $\newline$ Answer: $\square^{\circ}$