Question
An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle?
Round your answer to the nearest tenth.
0.4 radian
1.0 radian
2.7 radians
5.0 radians
Round your answer to the nearest tenth.
0.4 radian
1.0 radian
2.7 radians
5.0 radians
Ask by Hodgson Deleon. in the United States
Mar 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The angle measures approximately 2.7 radians.
Solution
Given:
- Arc length,
inches - Radius,
inches
The formula for the length of an arc is:
Where
Step 1: Solve for
Step 2: Substitute the given values:
Step 3: Calculate the value:
Step 4: Round to the nearest tenth:
Thus, the measure of the angle is
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To find the measure of the angle in radians, you can use the formula for the arc length
Plugging in the values we have:
Rounding to the nearest tenth, we get the answer approximately equal to 2.7 radians.
For a bit of extra fun, did you know that an angle of 2.7 radians corresponds to about 154.2 degrees? That’s nearly a right angle! Understanding radians can open up a world of geometry that connects beautifully with circles, oscillations, and waves. They’re like the secret sauce in math—it gives you such a deeper grasp of various phenomena!
