Question

Does anyone know how to some 4,5,6?

Answer 1

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°

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

`(-324)/(-540) = \text{cos C}\\\\\\(3)/(5)=\text{cos C}\\\\\\cos^(-1)\bigg((3)/(5)\bigg)=C`

53.1 ≈ C