Unit 10: Circles Name: Date: Per: Homework 3: Arc Lengths Directions: Find the measure of each bolded arc. Round to the nearest hundredth. 118 26 m 4. If TR = 11 # find the length of PS. 5. If MK = 10 m, find the length of MKL 3 6. YT’ = 28 in find the length of 172 7. AF = 23 cm, find the length
The Correct Answer and Explanation is :
To solve for the lengths of the arcs, you can use the formula for arc length, which is:
[
\text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r
]
Where:
- ( \theta ) is the central angle of the arc (in degrees).
- ( r ) is the radius of the circle.
- ( 2\pi r ) is the circumference of the circle.
Let’s break down each problem one by one:
- TR = 11, Find the length of PS:
If TR is given as 11, and PS is the same arc (TR), you would need the central angle of the arc in order to calculate its length. Without the angle ( \theta ), we cannot compute the exact arc length. If you were given the central angle, you would use the formula with the radius ( r ). - MK = 10 m, Find the length of MKL:
If MK is 10 m and MKL is a part of the circle, then it seems like MKL is a fraction of the full circle. If we assume MKL represents a specific central angle ( \theta ), we can apply the arc length formula once we know the angle. - YT’ = 28 in, Find the length of YT:
If the arc YT’ is given as 28 inches, you need the central angle and radius to determine the length of arc YT. With just the arc length, we still need more information about the central angle or the full circumference. - AF = 23 cm, Find the length of AF:
Assuming AF is the full arc length and we need to find it, we would again need the radius of the circle and the central angle.
Explanation:
The arc length depends on two variables: the central angle ( \theta ) and the radius ( r ). To calculate it precisely, you need both these values. If only the arc length is given, we need more context (like the full circle’s radius or angle) to apply the formula accurately.
In real-world problems, you may be given the central angle or radius explicitly, and sometimes the arc length is a fraction of the circle (like a quarter or half), which makes the calculation easier. When the angle is a fraction of 360°, the formula accounts for that by dividing ( \theta ) by 360°.
Would you be able to provide additional details like the central angles for these problems? That would allow for more precise answers.