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).

9.84763

Accepted Answer

Welcome back. Everyone in this problem. We want to determine the equivalent degree measure of 5.96536 radiance. We want to express our answer to the nearest minute for our answer choices. A is 683 degrees, 35 minutes. B is 512 degrees, 41 minutes. C is 170 degrees, 54 minutes and D is 341 degrees 47 minutes. Now, we want to determine our equivalent degree measure. OK? And our answer is written in radiance or our problem rather is written in radiance. So we need to ask ourselves, what do we know about the relationship between degrees and radiant measure? Well, recall, OK, that I read dance equals 180 degrees. That's something that we know. On the other hand, we have 5.96536 radiance from our problem. And we don't know how many degrees that is equal to. So we can now try and use this idea to help us solve for what we don't know because we notice that we could cross multiply here, right? And by doing that, we can find our unknown value because now that tells us our unknown value is going to be equal to 180 degrees multiplied by 5.96536 radiance, ok? And all of that is going to be divided by high radiance. So now we can go ahead and solve for our value of 5.96536 radiance in degrees. Now we can put this directly into our calculator. And when we do that, 180 multiplied by 5.96536 divided by pi will be equal to 341.79 degrees. Therefore, 5.96536 radiance is equivalent to 341.79 degrees. But we're not done yet. Remember that we want to write our answer to the nearest minute. No, we have a decimal part of our degree. That's 0.79. So we need to convert that into minutes. What do we know? Well, again, recall that one degree equals 60 minutes. So if we're going to convert 0.79 degrees into minutes, that means we need to multiply 60 minutes by 0.79. Ok. 0.79. Let me make that a little bit clearer here. So that's 0.79 times 60 minutes. Now, when we do that, what do we get? Well, when you put that into your calculator, you'll find that you get approximately 47 minutes and that's to the nearest minute. Ok. So now what does that tell us if we combine both of those parts together? Then it tells us that 5.96536 Radiance is equivalent to 341 degrees and 47 minutes. When we look back on our answer choices, that would have been answer choice. D 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).

9.84763

Key Concepts

Radian to Degree Conversion

Degrees and Minutes

Precision in Measurement

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