Convert each radian measure to degrees. Write answers to the n...

Question

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).

5

Accepted Answer

Welcome back. Everyone in this problem, we want to determine the equivalent degree measure of 19 radiant. And we want to express our answer to the nearest minute for our answer choices. A is 2177 degrees and 14 minutes. B is 1632 degrees and 56 minutes C is 1088 degrees and 37 minutes. And D is 544 degrees and 19 minutes. Now, if we're going to get the equivalent degree measure of 19 radiant, that means we have to understand the relationship between radiance and degrees. What do we know? Well, recall right, that py radians is equal to 180 degrees. No, that means 90 ingredients is going to be equal to a value that we don't. We don't really know yet. Ok. But we should be able to figure it out because we can cross multiply when we do that. Then that tells us our unknown value is going to be equal to 180 degrees multiplied by 19. Let me write that properly here multiplied by 19 radians divided by I radiance. No, we should be able to solve. So let's go ahead and do that. Now, 180 multiplied by 19 equals 3420. So our value for 19 radiant in degrees is going to be 3420 divided by pi degrees. Now let's get our calculator to help us from here because 3420 divided by pi that equals 1088.62. Therefore, 19 radiance is 1088.62 degrees. Now, we're almost there. But remember our problem wanted us to express our answer to the nearest minute. So we need to convert the fractional part of our degree. That's 0.62 into minutes. Now, what do we know? Well, we know that one degree is 60 minutes. So since one degree, right equals 60 minutes, then to find out how many minutes, 0.62 degrees equals we can multiply it by 60. So 0.62 let me write that below it, 0.62 degrees would be equal to 0.62 multiplied by 60 minutes. Now, what do we get when we do that? Well, 0.62 times 60 equals 37.2. So that would be 37.2 minutes. However, remember that we're writing our answer to the nearest minute. So to the nearest minute, 0.62 degrees would be approximately equal to 37 minutes. Therefore, that tells us then that 19 Radians in degrees is equal to 1088 degrees and 37 minutes. When we look back on our answer choices, that would have been answer choice. C Thanks a lot for watching everyone. I hope this video helped.

Convert each radian measure to degrees. Write answers to the nearest minute. See Example 2(c).

5

Key Concepts

Radian to Degree Conversion

Understanding Minutes in Angles

Precision in Measurement

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