Answer :
Sure! Let's solve this problem step by step:
1. Understand the given values:
- We have an arc length of 25 cm.
- The radius of the circle is 7 cm.
2. Recall the formula to find the angle subtended by an arc at the center of a circle:
- The angle in radians ([tex]\( \theta \)[/tex]) can be found using the formula:
[tex]\[ \theta = \frac{\text{arc length}}{\text{radius}} \][/tex]
3. Substitute the given values into the formula:
- Arc length = 25 cm
- Radius = 7 cm
[tex]\[ \theta = \frac{25 \, \text{cm}}{7 \, \text{cm}} \][/tex]
4. Calculate the angle in radians:
[tex]\[ \theta = \frac{25}{7} \approx 3.5714285714285716 \, \text{radians} \][/tex]
5. Convert the angle from radians to degrees:
- To convert radians to degrees, use the formula:
[tex]\[ \text{angle in degrees} = \theta \times \left(\frac{180}{\pi}\right) \][/tex]
- Here, [tex]\(\theta \approx 3.5714285714285716\)[/tex] radians.
[tex]\[ \text{angle in degrees} \approx 3.5714285714285716 \times \left(\frac{180}{\pi}\right) \][/tex]
[tex]\[ \text{angle in degrees} \approx 204.62778397529402 \][/tex]
So, the angle subtended by an arc of 25 cm at the center of a circle with a radius of 7 cm is approximately [tex]\( 3.5714285714285716 \)[/tex] radians or [tex]\( 204.62778397529402 \)[/tex] degrees.
1. Understand the given values:
- We have an arc length of 25 cm.
- The radius of the circle is 7 cm.
2. Recall the formula to find the angle subtended by an arc at the center of a circle:
- The angle in radians ([tex]\( \theta \)[/tex]) can be found using the formula:
[tex]\[ \theta = \frac{\text{arc length}}{\text{radius}} \][/tex]
3. Substitute the given values into the formula:
- Arc length = 25 cm
- Radius = 7 cm
[tex]\[ \theta = \frac{25 \, \text{cm}}{7 \, \text{cm}} \][/tex]
4. Calculate the angle in radians:
[tex]\[ \theta = \frac{25}{7} \approx 3.5714285714285716 \, \text{radians} \][/tex]
5. Convert the angle from radians to degrees:
- To convert radians to degrees, use the formula:
[tex]\[ \text{angle in degrees} = \theta \times \left(\frac{180}{\pi}\right) \][/tex]
- Here, [tex]\(\theta \approx 3.5714285714285716\)[/tex] radians.
[tex]\[ \text{angle in degrees} \approx 3.5714285714285716 \times \left(\frac{180}{\pi}\right) \][/tex]
[tex]\[ \text{angle in degrees} \approx 204.62778397529402 \][/tex]
So, the angle subtended by an arc of 25 cm at the center of a circle with a radius of 7 cm is approximately [tex]\( 3.5714285714285716 \)[/tex] radians or [tex]\( 204.62778397529402 \)[/tex] degrees.
A nice problem involving circular arc and angle!
Let's break it down step by step:
1. The radius of the circle is 7 cm.
2. The length of the arc is 25 cm.
3. We want to find the angle subtended by this arc at the center of the circle.
We can use the formula:
Angle (in radians) = Arc length / Radius
First, we need to convert the arc length from centimeters to radians:
1 radian = 360° / (2π) = 57.3° (approximately)
So, 25 cm is equal to:
25 cm × (2π) / (360°) = 0.436 radian (approximately)
Now, we can plug in the values:
Angle (in radians) = 0.436 radian
= Arc length / Radius
= 25 cm / 7 cm
= 0.357 radian (approximately)
To convert the angle from radians to degrees, we multiply by 180°/π:
Angle (in degrees) = 0.357 radian × (180°/π) ≈ 20.4°
So, the angle subtended by the arc of 25 cm at the center of the circle is approximately 20.4°.
Let's break it down step by step:
1. The radius of the circle is 7 cm.
2. The length of the arc is 25 cm.
3. We want to find the angle subtended by this arc at the center of the circle.
We can use the formula:
Angle (in radians) = Arc length / Radius
First, we need to convert the arc length from centimeters to radians:
1 radian = 360° / (2π) = 57.3° (approximately)
So, 25 cm is equal to:
25 cm × (2π) / (360°) = 0.436 radian (approximately)
Now, we can plug in the values:
Angle (in radians) = 0.436 radian
= Arc length / Radius
= 25 cm / 7 cm
= 0.357 radian (approximately)
To convert the angle from radians to degrees, we multiply by 180°/π:
Angle (in degrees) = 0.357 radian × (180°/π) ≈ 20.4°
So, the angle subtended by the arc of 25 cm at the center of the circle is approximately 20.4°.
