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).

0.3417

Accepted Answer

Welcome back. Everyone in this problem, we want to determine the equivalent degree measure of 0.5629 to the nearest minute. For our answer choices. A is 64 degrees and 30 minutes B is 16 degrees and eight minutes C is 32 degrees, 15 minutes and D is 48 degrees 23 minutes. Now, we're trying to find the equivalent degree measure of 0.5629 radiance. So first, we have to ask ourselves, what do we know about degrees and radiance? Well, recall that Py radians, OK, equals 180 degrees. That's what we know. And now we have 0.5629 degrees radiance. Sorry, but we don't know how many degrees it's equal to. So how can we figure it out? Well, here, we could cross multiply because if we cross multiply, then we could solve for our unknown value. So let's do that doing that. That tells us then that our unknown value equals 0.5629 radiance multiplied by 180 degrees all divided by high radiance. Now, we can go ahead and convert to degrees if we put 0.5629 multiplied by 180 in our calculator. OK. And divided by pi radiance, we'll find that we get 32.25 degrees. So in other words, 0.5629 radiance is equivalent to 32.25 degrees. No, we are almost there. But remember, we are writing our answer to the nearest minute. We know that since our degree has a decimal part, we need to convert the decimal part to minutes. Recall again, recall that one degree equals 60 minutes. So if we're going to convert 0.25 degrees to minutes, it means we're going to multiply 0.25 by 60 minutes, 0.25 multiplied by 60. That's the same thing as a quarter of 60 which equals 15. So 0.25 degrees is equivalent to 15 minutes. Therefore, if we combine both parts, that now means that 0.5629 radiance, ok? Is equivalent to 32 degrees and 15 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).

0.3417

Key Concepts

Radian to Degree Conversion

Understanding Minutes in Angles

Precision in Measurement

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