Find the length of side c.

Given:
a = 16
b = 30
Angle C = 30°

Law of Cosines: c² = a² + b² - 2ab * cos(C)

Round your final answer to the nearest tenth.

Using the Law of Cosines, the length of side c was calculated to be approximately 18.0. This involved substituting the known values and computing step by step. The final result is rounded to the nearest tenth.
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Answered by LiamAlexanderSmith | 2025-07-22

To find the length of side c using the Law of Cosines, we can apply the formula:
c 2 = a 2 + b 2 − 2 ab ⋅ cos ( C )
Here, we have the following values:

a = 16

b = 30

C = 3 0 ∘


Step 1: Substitute the given values into the formula.
c 2 = 1 6 2 + 3 0 2 − 2 ⋅ 16 ⋅ 30 ⋅ cos ( 3 0 ∘ )
Step 2: Calculate each square.
1 6 2 = 256
3 0 2 = 900
Step 3: Calculate cos ( 3 0 ∘ ) .
The cosine of 3 0 ∘ is 2 3 ​ ​ or approximately 0.866.
Step 4: Substitute cos ( 3 0 ∘ ) and perform the calculation.
c 2 = 256 + 900 − 2 ⋅ 16 ⋅ 30 ⋅ 0.866
c 2 = 256 + 900 − 831.36
c 2 = 1125.36 − 831.36
c 2 = 294
Step 5: Find c by taking the square root of 294 .
c = 294 ​ ≈ 17.1
Rounding to the nearest tenth, the length of side c is approximately 17.1.

Answered by LiamAlexanderSmith | 2025-07-22