How to find arc length with circumference and central angle

Asked by admin @ 29/10/2021 in Mathematics viewed by 279 People

Find the measure of the central angle.

the circle has a circumference of 9 and the arc length is 1. Use 3.14 for pie.

Answered by admin @ 29/10/2021

To start with we have to write down what we know. pi=3.14, r=9, arc length is 1. x is the angle we are trying to find. Saying that the radius is 9

There is an equation that states that the arc length is equal to x/360 (the fraction of the circle) multiplied by the circumference or 2 times pi times the radius.
$L= \frac{x}{360} * 2 \pi r$
where * means multiply.
$1= \frac{x}{360} * 3.14 * 9$
Simplify
$1= \frac{x}{360} *28.26$
Take the 28.26 over to the other side of the equation, where it then it divides the 1.
$\frac{1}{28.26} = \frac{x}{360}$
This becomes: $0.035= \frac{x}{360}$
Then the 360 is brought over to the other side and multiplies the 0.035:
$360*0.035=x$
And finally simplify the whole equation and we get our answer.
$x=12.739 degrees x=12.7 degrees$

How to find arc length with circumference and central angle

Similar Questions

How to find radius with arc length and central angle

How to find length of right triangle with only angles

How to find the length of a triangle using angles

Arc ab is of the circumference of a circle. what is the radian measure of the central angle?

Arcs semicircles and central angles worksheet answers a 6 1

How to find the actual length of a scale drawing

Find the length of side x in the right triangle

How to find sum of interior angles of a polygon

How to find the missing angle of a right triangle

4 2 practice find the measure of each numbered angle

How to find the missing angle of an isosceles triangle

How do you find the missing angle of a triangle

Find the missing angle of a right triangle using trigonometry

How to find sum of interior angles in a polygon

How do u find the missing length of a triangle

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

All things algebra unit 7 polygons and quadrilaterals answer key

Gina wilson all things algebra 2016 answer key unit 11

Unit 1 geometry basics homework 4 angle addition postulate answers

Unit 6 exponents and exponential functions homework 8 answer key

The manager of a vacation resort believes that the ages

What is 271 403 rounded to the nearest ten thousand

Unit 1 geometry basics homework 3 angle relationships answer key

Homework 2 parallelograms

Why would a prism beat a sphere in a competition?

John wants to send a letter to peter

An artist sells a painting for 20.50 but uses 5.75

Unit 4 congruent triangles homework 1 classifying triangles answer key

Unit 4 congruent triangles homework 2 angles of triangles

Compare the values of the 2s and 5s in 55220