I'll solve both example problems step by step using the Law of Cosines.
## Problem 1: Find side x
Given: Two sides (7 and 5) and the included angle (58°)
Step 1: Identify what we have and what we need
- Side a = 7
- Side b = 5
- Angle C = 58° (the angle between the two sides)
- We need to find side c = x
Step 2: Use the Law of Cosines formula
c² = a² + b² - 2ab cos(C)
Step 3: Substitute the values
x² = 7² + 5² - 2(7)(5)cos(58°)
Step 4: Calculate each part
- 7² = 49
- 5² = 25
- 2(7)(5) = 70
- cos(58°) ≈ 0.5299
x² = 49 + 25 - 70(0.5299)
x² = 74 - 37.093
x² = 36.907
Step 5: Take the square root
x = √36.907
x ≈ 6.075
Let me verify this calculation:
Parent Tip: Review the logic above to help your child master the concept of the law of cosines worksheet.
