I know that I'm using the Law of Cosines, but I'm confused on how to solve. I have to also round my answers to the nearest tenth for degrees and to the nearest hundredth for sides.

Given:
A= 55 degrees
b=3
c=10

Find:
a=
B=
C=

To solve the Law of Cosines problem, we will use the formula:

c^2 = a^2 + b^2 - 2ab*cos(C)

Given that c = 10, b = 3, and C is currently unknown, let's start by finding the value of C.

1. Rearrange the formula to solve for cos(C):
cos(C) = (a^2 + b^2 - c^2) / (2ab)

2. Plug in the known values:
cos(C) = (a^2 + 3^2 - 10^2) / (2 * a * 3)

3. Simplify the equation:
cos(C) = (a^2 + 9 - 100) / (6a)
cos(C) = (a^2 - 91) / (6a)

4. Apply the value of cos(C) to a calculator to find the angle C: (cos^(-1))^-1 = arccos
C = arccos((a^2 - 91) / (6a))

5. Use the given angle A to find B:
B = 180 - A - C

6. Substitute the value of B and C into the formula: (Law of Sines)
a / sin(A) = b / sin(B) = c / sin(C)

7. Solve for a using the formula:
a = sin(A) * (c / sin(C))

To solve for the missing side and angles using the Law of Cosines, follow these steps:

1. Write down the Law of Cosines formula:
c^2 = a^2 + b^2 - 2abcos(C)

2. Identify the given values:
Let A = 55 degrees, b = 3, c = 10

3. Solve for the missing side 'a':
Using the Law of Cosines, we can rearrange the formula to solve for 'a':
a^2 = c^2 + b^2 - 2bc*cos(A)
Substituting the given values:
a^2 = 10^2 + 3^2 - 2(10)(3)*cos(55)
a^2 = 100 + 9 - 60*cos(55)

Now, to solve for 'a', you need to evaluate cos(55) using a calculator or online trigonometric tool. Substitute the value into the equation and take the square root of both sides. Round the answer to the nearest hundredth to match the rounding requirement mentioned.

4. Solve for the missing angle 'B':
To find angle B, we will use the Law of Cosines again:
cos(B) = (a^2 + c^2 - b^2) / (2ac)
Substitute the known values:
cos(B) = (a^2 + 10^2 - 3^2) / (2*a*10)

Now, solve for cos(B) by substituting the value of 'a' that you obtained from the previous step into the equation. Once you have cos(B), take the inverse cosine (cos^(-1)) to find the angle B. Round the answer to the nearest tenth to match the given rounding requirement.

5. Solve for the missing angle 'C':
Angle C can be found by subtracting angles A and B from 180 degrees since the sum of all angles in a triangle is 180 degrees. Round the answer to the nearest tenth to match the given rounding requirement.

By following these steps, you can solve for the missing side 'a' and the missing angles 'B' and 'C' using the Law of Cosines.