Convert each degree measure to radians. If applicable, round t...

Question

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

174° 50'

Accepted Answer

Welcome back. I am so glad you're here. We're asked to determine the equivalent radiant measure of 165 degrees 40 minutes. We're asked to express the answer to the nearest 1000th. Our answer choices are answer choice. A 1.446 answer choice, B 2.891 answer choice. C 5.783 and answer choice D 4.891. All right. So we need to convert from degrees to radiance. But before we can do that, we actually need to take some time and convert from minutes to degrees. We have these 40 minutes. Well, we can do that with unit conversion. We recall from previous lessons that there are 60 minutes in one degree. So 60 minutes is equal to one degree. If we take 40 minutes and multiply that by the unit, we'll put one degree in the numerator divided by 60 minutes in the denominator. Now, our minutes units cancel out and we can multiply straight across 40 multiplied by one degree is 40 then degrees. And that's divided by 60 in the denominator. Now, we can simplify 40 divided by 60. Simplifies to two thirds. So we have two thirds degrees. And what that means is we have 165 degrees plus another two thirds of a degree. And we want to combine these, so you can get your common denominator skills out and combine those or you can put into your calculator 165 plus two thirds. And we get 497 divided by three degrees. So there is our 165 degrees 40 minutes expressed only in degrees 497 divided by three. Now, we can convert to radiance. So we recall from previous lessons that when we're converting from degrees to radiance, we're going to multiply by the unit again, with unit conversion we'll have in the numerator pi radiance that's divided by in the denominator 180 degrees. Now, our degree units cancel out, we can multiply straight across in the numerator. We have 490. I'm writing that wrong 497 pi divided by, in the denominator three multiplied by 180 is 540 and this is radiance. And because they want the answer expressed to the nearest 1000th, you can plug that into a calculator 497 pi divided by 540. And that gets us 2.8914 that keeps going, but we're rounding to the 1000th. That's the third decimal place. Looks to the four, it's going to stay a one. So we have 2.891 radiance. And that's our equivalent radiant measure of 165 degrees 40 minutes. We look at our answer choices and this matches with answer choice. B well done. We'll catch you on the next one.

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

174° 50'

Key Concepts

Degree to Radian Conversion

Understanding Minutes in Angles

Rounding Numbers

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