Find the length of the arc on a circle of radius 20 feet intercep...

Question

Find the length of the arc on a circle of radius 20 feet intercepted by a 75° central angle. Express arc length in terms of 𝜋. Then round your answer to two decimal places.

Accepted Answer

Hello, today we're going to be solving the following arc length problem. So we are told that we want to calculate the arc length of a circle with a radius of 32 m. A central angle of 82 degrees intercepts the arc. We want to write the answer in terms of pi and in a decimal form rounded to the nearest 100th. So how can we calculate the arc length of a circle? Well, we have an equation for the arc length and it is given to us as S is equal to R multiplied by the. Here R represents the radius of the circle and data represents a central angle. The problem tells us that the radius is 32 m. So we can set R equal to 32 m. And the problem tells us that the central angle is 82 degrees. So we can set data equal to 82 degrees. Now, one thing to note is that we want the arc length to be in terms of pie in order to get an answer in terms of pi we'll need to convert our data from degrees to radiance in order to do this we can multiply 82 degrees by the quantity pi over 1 multiplying these quantities together will give us 82 pi over 1 80. And this quantity will simplify to leave us with 41 pi over 90. So we have the as 41 pi over 90 we have R as 32 m. If we plug this into the equation of the length of an arc that will give us s as equal to 32 m multiplied by 41 pi over 90 multiplying these quantities together will give us pi over 90 m. And this will simplify to leave us with 656 pi over 45 m. So this is the length of the arc in terms of pie. But keep in mind that the problem asks us to re write the answer in a decimal form rounded to the nearest 100th. If we were to plug this into a calculator and round to the nearest 100th, we'll get an arc length of approximately 45. m. So the length of the arc in terms of pi is 656 pi over 45 m. And in decimal form is approximately 45.80 m. With that being said, the answer to this problem is going to be D 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 of the arc on a circle of radius 20 feet intercepted by a 75° central angle. Express arc length in terms of 𝜋. Then round your answer to two decimal places.

Key Concepts

Arc Length Formula

Conversion from Degrees to Radians

Rounding and Expressing in Terms of π

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