Answered

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Explanation:

Provided 2 length sides and one angle also need to find one missing side.

So, use cosine rule:

a² = b² + c² - 2bc cos(A)

Part 1

c² = 9² + 11² - 2(11)(9) cos(57)

c² = 94.16147

c = √94.16147 = 9.70 cm

Part 2

d² = 5² + 7² - 2(5)(7) cos(48)

d² = 27.16

d = √27.16 = 5.21

Part 3

5² = 7² + 9² - 2(7)(9) cos(H)

-126cos(H) = 25 - 49 - 81

cos(H) = -105/-126

cos(H) = 5/6

H = cos⁻¹(5/6) = 33.56°

Part 4

8² = 4² + 7² - 2(4)(7) cos(J)

-56cos(J) = 64 - 16 - 49

cos(J) = -1/-56

J = cos⁻¹(1/56) = 88.98°

Passcode: 3142

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