Pregunta
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
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The angle measures approximately 2.7 radians.
Solución
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
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Simplifique esta solución 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!
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