Help Please? Law of Cosines Problem.

Question

Use the Law of Cosines to determine the indicated side x. (Assume b = 19 and c = 21. Round your answer to one decimal place.)

x = 1

Answer 1

Hey Kayley E.,

Let's start by referring to the law of cosines: c² = a² + b² − 2ab cos(C). Since we are looking for an unknown side length, we will have to use the value A as our C in the equation, x as c, and c as a. Don't let this confuse you, all we are doing is recognizing corresponding variables for our own convenience. Let's plug in the numbers:

1. x² = c² + b² − 2cb cos(A)
2. x² = 21² + 19² − 2(21)(19) cos(108°)
3. x² = 1048.6
4. √x² = √1048.6
5. x = 32.382

I hope this helps, let me know if you have any questions.

Answer 2

Hey Kayley!

Let's review the law of cosine before using it. The law of cosine says a²=b²+c² – 2*b*c*cos(A). In our case a=x.

So, let's plug in the given values.

x²=19²+21² – 2*19*21*cos(108°). (This is a common mistake point! Make sure your calculator is using degrees and not radians!)

So,

x² = 1048.59, so now we need to take the square root of both sides to get x. So, x = 32.38.

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