### Arc Length Calculation**Problem:**23. What is the length of an arc having a radius of curvature of 12 and an angle measure of 226 degrees?**Solution Explanation:**To find the length of an arc (L) with a given radius (r) and central angle (θ), you can use the formula:\[ L = r \times \theta \]However, the angle θ must be in radians. To convert degrees to radians, use the conversion factor:\[ \text{Radians} = \text{Degrees} \times \left( \frac{\pi}{180} \right) \]Applying this conversion to the given angle of 226 degrees:\[ \theta = 226 \times \left( \frac{\pi}{180} \right) \]\[ \theta = 226 \times \left( \frac{3.14159}{180} \right) \]\[ \theta \approx 3.945 \, \text{radians} \]Now, using the radius $ r = 12 $:\[ L = 12 \times 3.945 \]\[ L \approx 47.34 \]Therefore, the length of the arc is approximately 47.34 units.

Given Radius = 12 Angle = 226 degree

Answered: 23. What is the length of an arc having…

Math

Algebra

23. What is the length of an arc having a radius of curvature of 12 and an angle measure of 226 degrees ? *

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

See similar textbooks

Related questions

Q: 24. A wheel makes 2 revolutions with a distance of 176 m. What is the radius of the 22 wheel? (Taken…

Q: The length L of a long wall is to be approximated. The angle 0, as shown in the diagram (not to…

A: To find the length of the perpendicular side L of a right-angled triangle when you have the base…

Q: · What is the length of an arc of a circle that intercepts angle 45° in a c. rcle of radius 40 cm?…

Q: 8. What is the slant height of a cone if the radius is 5mm and the surface area 7. 18 mi is 55rmm??…

A: surface area means total surface area of cone. Formula to find the surface area of cone is A=πr2+πrl…

Q: 10) The 10 cm segment is part of a line tangent to circle O. Solve for: the nearest tenth. Briefly…

Q: 14. Using the cosine law, calculate the length of side b, to the nearest tenth. (a) 7.5 (b) 5.6. 102…

Q: 3. What is the exact circumference of a circle that has a radius of 5 cm?

A: Given Radius of the circle r = 5cm Circumference of any circle C = 2 * π * r

Q: Use trigonometry to find the measure of the arc cut off by a chord 12 cmlong in a circle of radius…

A: Given, The length of the chord is 12 cm, The radius of the circle is 10 cm.

Q: 5. What is the area of the 4-petal flower? The square is 10 cm by 10 cm, and the curves are from…

A: Area of region

Q: Radius of OQ A 187 in. B.

Q: Draw a circle of diameter 5.6 cm with centre C. i) Draw a chord not passing through the centre.

Q: Define the term 'construction of circle'?

A: Circle: The circle is the set of points that are at equal distance from a given point. Construction…

Q: Is triangle P'R'S' a dilation of triangle PRS? Explain why or why not.

A: We have to explain if triangle P'R'S' is a dilation of triangle PRS.

Q: 9. Use the formula for arc length to find the circumference of the circle x2 +y2 = 4.

A: The equation of a circle, with the centre as the origin is, X2 + Y2 = a2 Where, a =…

Q: 21. The measure of the longest cord on a circle is 20 cm. What is the measure of its radius? a. 5 сm…

A: We have to find measure of radius of circle where measure of the longest chord on a circle is 20 cm.…

Q: Find the length of AR in this circle, leave your answer in terms of T. DB is the diameter with a…

Q: 26. Find the area of the trapezoid. 18' noi 37' 12'-3"

Q: 43. What is the angle between the base of a cubical glass paperweight and a diagonal of the cube…

A: Follow the procedure given below.

Q: 0° arc of circle A has the same length as a 45° arc of circle B. What is the o of the radius of…

A: Given query is to find the ratio of the radius.

Q: 1. A trough is 1m long and its cross section is a triangle which is 3m high and 2m wide across the…

A: The shape of the trough is like a prism, which has a cross-section and height. The area of the prism…

Q: What is the degree measu circle?

A: Here we have to find the angle between the radius or diameter and chord of the circle.

Q: 11. Find the length of the radius BC ao

A: It is not clear in the figure that if the perpendicular is 6 or 9 hence answering by cases taking…

Q: sphere has a great circle with a circumference of 330 centimeters. (a) What is the radius of the…

Q: What is the area of the circle in terms of

A: Area of the circle =π r2Radius of the given circle:r=4.6 mArea=π(4.6)2 m2Area= 21.16π m2

Q: 13.A chord is 16 units from the center of a circle. The radius of the circle is 20 units. What is…

A: Given Data: The distance of the chord from the centre of the circle is: d=16 units The radius of the…

Question

100%

### Arc Length Calculation

**Problem:**
23. What is the length of an arc having a radius of curvature of 12 and an angle measure of 226 degrees?

**Solution Explanation:**

To find the length of an arc (L) with a given radius (r) and central angle (θ), you can use the formula:

\[ L = r \times \theta \]

However, the angle θ must be in radians. To convert degrees to radians, use the conversion factor:

\[ \text{Radians} = \text{Degrees} \times \left( \frac{\pi}{180} \right) \]

Applying this conversion to the given angle of 226 degrees:

\[ \theta = 226 \times \left( \frac{\pi}{180} \right) \]
\[ \theta = 226 \times \left( \frac{3.14159}{180} \right) \]
\[ \theta \approx 3.945 \, \text{radians} \]

Now, using the radius $ r = 12 $:

\[ L = 12 \times 3.945 \]
\[ L \approx 47.34 \]

Therefore, the length of the arc is approximately 47.34 units.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Area of a Circle$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

8. Find the length of each arc if the radius is equal to one. Do not use decimals in your answer
7. Match the parts of a circle, • 1. A a. Radius b. Chord - 2. B c. diameter - 3. D d. Minor Arc • 4. c e. Center of the Circle - 5. 0
What’s the answer to this question?
9. The manufacturer of a propeller for a small aircraft rotates at 3600 rpm. The tips are located 8m away from the centre of the propeller. Determine the length of the arc travelled by one tip of the propeller in 0.0005s.
Note: Kindly provide a solution pls. The answer is already provided. Thank you! 1.13 The length of arc of a circle subtended by an inscribed angle ABC of 56° is equalto 37.51 cm. Compute the area (cm^2) of the triangle ABC. Ans: 475.97
4. A circle is circumscribed about an equilateral triangle of area 12/3. Find the area of the circle.