Hi I'm reviewing the following solution in my trigonometry text book and I can't figure out how they got their answer. If someone can help explain how they calculated 542.25 for a^2 (nothing I do comes up with that number):

a2=b2+c2-2bcCosA
a2=(16)^2+(11)^2 -2(16)(11)Cos118
a2=542.25
|a2=|542.25
a=23.3

Thank you!

I got exactly that.

a^2= 16^2 + 11^2 - 2(16)(11)cos118°
= 256 + 121 - 352(-.469471562)
= 377 + 165.2539898
= 542.253989
a = √542.2539898
= 23.2863

Are you following the order of operation?

Thank you, I think it was how I was using my calculator. I didn't add brackets, now I got the same too. Very helpful to have that extra confirmation, I can't tell you how long I've been stuck on this question. Thanks a million!

To understand how the value of 542.25 was calculated for a^2, let's break down the steps:

Step 1: Start with the formula a^2 = b^2 + c^2 - 2bcCosA.
This formula is derived from the Law of Cosines, which relates the side lengths of a triangle to the cosine of one of its angles.

Step 2: Substitute the given values for b, c, and A into the formula.
In the given problem, we are given the values b = 16, c = 11, and A = 118 degrees. Substituting these values into the formula, we get:
a^2 = (16)^2 + (11)^2 - 2(16)(11)Cos(118)

Step 3: Simplify the expression.
Using the rules of arithmetic, simplify the expression:
a^2 = 256 + 121 - 2(16)(11)Cos(118)

Step 4: Calculate the cosine of 118 degrees.
To find the value of Cos(118), you can use a scientific calculator or trigonometric table. The cosine of 118 degrees is -0.469471.

Step 5: Substitute the value of Cos(118) into the equation.
Now substitute the value of Cos(118) = -0.469471 into the expression:
a^2 = 542.25

Step 6: Solve for a.
To find the value of a, take the square root of both sides of the equation:
√(a^2) = √542.25
a = ±23.3

Note: We typically take the positive root when dealing with side lengths, so the solution is a = 23.3.

So, the value of 542.25 for a^2 is obtained by following the steps outlined above.