Use the Law of Cosines
NOTE: Please check my numbers. The numbers were blurry in the picture.
Answer: 4) b = 29.8
5) a = 24.3
6) C = 53.1°
Step-by-step explanation:
4)
b² = a² + c² - 2ac · cos B
= (20)² + (25)² - 2(20)(25) · cos 82°
= 400 + 625 - 1000 (0.139)
= 888
√b² = √888
b ≈ 29.8
5)
a² = b² + c² - 2bc · cos A
= (18)² + (28)² - 2(18)(28) · cos 59°
= 324 + 784 - 1008 (0.515)
= 590.49
√a² = √590.49
a ≈ 24.3
6)
c² = a² + b² - 2ab · cos C
15² = (15)² + (18)² - 2(15)(18) · cos C
225 = 225 + 324 - 540 cos C
[tex]\dfrac{-324}{-540} = \text{cos C}\\\\\\\dfrac{3}{5}=\text{cos C}\\\\\\cos^{-1}\bigg(\dfrac{3}{5}\bigg)=C[/tex]
53.1 ≈ C
