Question

find the length of the arc indicated in bold. leave your answer in terms of pi. radius 7 yards angle measure is 105

Answer 1

r u sure

Answer 2

To find the length of an arc, you can use the formula:

\[
L = r \theta
\]

where:
- \( L \) is the length of the arc,
- \( r \) is the radius of the circle,
- \( \theta \) is the angle in radians.

First, we need to convert the angle from degrees to radians. The conversion from degrees to radians is given by:

\[
\theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180}
\]

For your angle of 105 degrees:

\[
\theta_{\text{radians}} = 105 \times \frac{\pi}{180} = \frac{105\pi}{180} = \frac{7\pi}{12}
\]

Now substituting the values into the arc length formula:

\[
L = r \theta = 7 \times \frac{7\pi}{12} = \frac{49\pi}{12}
\]

Thus, the length of the arc is:

\[
\frac{49\pi}{12} \text{ yards}
\]

Answer 3

Yes, let's double-check the calculations step-by-step for clarity.

1. **Angle Conversion**:
The angle given is 105 degrees. To convert this angle to radians, we use the formula:

\[
\theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180}
\]

Substituting in the angle:
\[
\theta_{\text{radians}} = 105 \times \frac{\pi}{180} = \frac{105\pi}{180}
\]

Simplifying this fraction:
\[
\frac{105\pi}{180} = \frac{7\pi}{12}
\]

2. **Arc Length Calculation**:
The formula for the length of the arc is:
\[
L = r \theta
\]

Here, the radius \( r = 7 \) yards and the angle \( \theta = \frac{7\pi}{12} \):

\[
L = 7 \times \frac{7\pi}{12} = \frac{49\pi}{12}
\]

Thus, the length of the arc is indeed:

\[
\frac{49\pi}{12} \text{ yards}
\]

So, the calculations are accurate. The length of the arc is \( \frac{49\pi}{12} \) yards.