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.

8. Given a = 11, C = 131 degrees, and b = 8, use the Law of Cosines to solve for c. Round your answer to the nearest tenth.

9. Given c = 9.6, b = 5.9, and a = 10.5, use the Law of Cosines to solve for C. Round your answer to the nearest degree.

Answer 1

Answer:

A.

B.

C.

Explanation:

We have been given inverse trigonometric functions. We are asked to find the value of each function.

A.

We will use inverse sin to solve our given equation as:

Round to nearest degree:

B.

We will use inverse tann to solve our given equation as:

Round to nearest degree:

C.

We will use inverse cosine to solve our given equation as:

Round to nearest degree:

Explanation:

Answer 2

Answer: (7) 7.0 (8) 17.3 (9) 64.7°

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 =
`√(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 =
`√(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