Find the length to three significant digits of each arc intercept...

Question

Find the length to three significant digits of each arc intercepted by a central angle  in a circle of radius r. See Example 1.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          r = 1.38 ft , θ = 5π/6 radians

Accepted Answer

Hello, today we're going to be determining the arc length with the given central angle and the radius of the circle. And we want to express our answer to two decimal places. So what is going on is that we have a circle, this circle has a central angle theta. Now the angle theta that is given to us is theta that is equal to seven pi divided by eight radiant. So our angle theta is given to us in terms of radiance, we are also told that the circle has a radius of 4.56 ft. We want to use this information to determine the length of the arc that is formed by the central angle. So how can we go about doing this? Well, we have the equation that is given to us for the arc length of a circle. The arc length of a circle is defined as S is equal to R multiplied by theta. This is where R represents the radius of the circle and the is the angle in terms of radiance. So we already know that our data is given to us in terms of radiance. And we are given the radius of the circle. We have the information we need to find the arc length. So we're just gonna be plugging in this information into the equation that will give us ss equal to the radius which is 4.56 ft multiplied by the central angle theta which is seven pi divided by 84.56 multiplied by seven pi divided by eight will give us the value of 31.92 pi divided by ft. Now, at this point, I would recommend plugging in this value into a calculator. And when you do so, we're going to end up with a very lengthy decimal. The arc length will currently equal to 12.53495 and so 1 ft, what we're going to do is we're going to round this decimal to two decimal places. So we're going to be taking a look at the number to the right of three. This number is less than five. So we're going to keep the three as it is. And with that being said, the final arc length for the circle will be 12.53 ft. And with that being said, the answer to this problem is going to be c So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1. r = 1.38 ft , θ = 5π/6 radians

Key Concepts

Arc Length Formula

Radians vs. Degrees

Significant Figures

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