Question

7. Given b= 4, c = 10, and A = 34 degrees, use the Law of Cosines to solve for a. Round your answer to the nearest whole number.

Answer 1

Answer:  (7) 7.0              (8) 17.3            (9) 64.7°

Step-by-step explanation:

Law of Cosines is: a² = b² + c² - 2bc · cos A

                         or: b² = a² + c² - 2ac · cos B

                         or: c² = a² + b² - 2ab · cos C

7) b = 4, c = 10, ∠A = 34

a² = b² + c² - 2bc · cos A

   = 4² + 10² - 2(4)(10) · cos 34°

   = 16 + 100 - 80 (0.829)

   = 116 - 66.323

   = 49.677

a = $\sqrt{49.677}$

a = 7.0

8) a = 11, b = 8, ∠C = 131

c² = a² + b² - 2ab · cos C

   = 11² + 8² - 2(11)(8) · cos 131°

   = 121 + 64 - 176 (-0.656)

   = 185 + 115

   = 300

c = $\sqrt{300}$

c = 17.3

9) a = 10.5, b = 5.9, c = 9.6

9.6² = 10.5² + 5.9² - 2(10.5)(5.9) · cos C

92.16 = 110.25 + 34.81 - 2(10.5)(5.9) · cos C

92.16 = 145.06 - 123.9 cos C

-52.9 = -123.9 cos C

0.427 = cos C

cos⁻¹ (0.427) = C

64.7° = C