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 for the missing values using the Law of Cosines, follow these steps:

Step 1: Identify which sides and angles are given. In this case, you are given angle A, side b, and side c. You are asked to find side a, angle B, and angle C.

Step 2: Use the Law of Cosines formula:

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

where c is the side opposite angle C. Rearrange the formula to solve for side a:

a^2 = c^2 + b^2 - 2cb * cos(A)
a = sqrt[c^2 + b^2 - 2cb * cos(A)]

Step 3: Substitute the given values into the formula:

a = sqrt[(10^2) + (3^2) - 2(10)(3) * cos(55°)]
a = sqrt[100 + 9 - 60 * cos(55°)]
a = sqrt[109 - 60 * 0.5736]
a = sqrt[109 - 34.416]
a = sqrt[74.584]
a ≈ 8.6 (rounded to the nearest hundredth)

Step 4: To find angle B, use the Law of Cosines again:

cos(B) = (a^2 + c^2 - b^2) / (2ac)
B = arccos[(a^2 + c^2 - b^2) / (2ac)]

Substitute the known values:

B = arccos[(8.6^2 + 10^2 - 3^2) / (2 * 8.6 * 10)]
B = arccos[(73.96 + 100 - 9) / 172]
B = arccos[164.96 / 172]
B = arccos[0.959]

Using a calculator, find the inverse cosine (arccos) of 0.959:
B ≈ 15.3° (rounded to the nearest tenth)

Step 5: To find angle C, simply subtract angles A and B from 180°:

C = 180° - A - B
C = 180° - 55° - 15.3°
C ≈ 109.7° (rounded to the nearest tenth)

Therefore, the solutions are:
a ≈ 8.6, B ≈ 15.3°, and C ≈ 109.7°