[Technology Exercise]

You wa...

Question

[Technology Exercise]

You want to make an 80° angle by marking an arc on the perimeter of a 12-in.-diameter disk and drawing lines from the ends of the arc to the disk’s center. To the nearest tenth of an inch, how long should the arc be?

Accepted Answer

Hi everyone. Let's take a look at this practice problem. This problem says in a clock, the minute hand is 4 inches long. To calculate the distance traveled by the tip of the minute hand from 12 o'clock to 2 o'clock, which is a 60 degree angle, to the nearest 10th of an inch, what would be the length of the arc? We're given 4 possible choices as our answers. For choice A, we have 2.1 inches. For choice B, we have 4.2 inches. For choice C, we have 6.3 inches, and for choice D, we have 8.4 inches. Now, we need to calculate the arc length that this minute hand has traveled. So we call your definition for arc length, which we'll label as S, and that's going to be equal to the radius R, multiplied by the angle theta in radiance. Now, if we look at the information that we're given, the problem, we're told that the minute hand is 4 inches long. So that means that our radius R is going to be equal to 4 inches. And the angle that we're going to be using is going to be the 60 degree angle. However, we need this in radiance. So theta is going to be equal to 60 degrees, and here you need to recall your conversion factor from degrees to radiance. So we'll need to multiply this by the convergent factor of pi divided by 180 degrees. And when we evaluate this expression, this is going to be equal to pi divided by 3. So we'll substitute in our values for R and theta into our formula for the arc length. And so this is going to be equal to 4 inches. Multiplied by pi divided by 3. And when we evaluate this expression, this is going to be equal to 4.2 inches. So here we've just rounded to one decimal place, since that is what The question asks us to do. So this is the answer that we're looking for, and if we compare our answer to our answer choices, we see that the correct answer choice corresponds to answer choice B. So, I hope that this explanation has been useful, and I'll see you in the next video.

[Technology Exercise]

You want to make an 80° angle by marking an arc on the perimeter of a 12-in.-diameter disk and drawing lines from the ends of the arc to the disk’s center. To the nearest tenth of an inch, how long should the arc be?

Key Concepts

Arc Length

Circle Geometry

Radians vs. Degrees

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