Question

Please help me with his math question ​

Answer 1

Answer:  ∠A = 55° (acute)

               ∠B = 105° (obtuse)

               ∠C = 86° (acute)

               ∠D = 114° (obtuse)

Step-by-step explanation:

Use Law of Cosines: a² = b² + c² - 2bc · cosA     for each of the angles.

Note that ∠B from each triangle will have to be added to solve for ∠B.

Similarly for ∠D.

For ΔDAB: a = 9.1, b = 7.3, d = 11

9.1² = 7.3² + 11² - 2(7.3)(11) · cosA

82.81 = 53.29 + 121 - 160.6 · cosA

-91.48 = -160.6 cosA

0.5696 = cos A

55° = A

b² = a² + c² - 2ac · cosB

7.3² = 9.1² + 11² - 2(9.1)(11) · cosB

53.29 = 82.81 + 121 - 200.2 · cosB

-150.52 = -200.2 cosB

0.7518 = cosB

41° = B

ΔDAB: ∠A + ∠B + ∠D = 180°

            55° + 41° + ∠D = 180°

                 96°    + ∠D = 180°

                              ∠D = 84°

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For ΔBCD: b = 8.2, c = 9.1, d = 4.6

b² = c² + d² - 2cd · cosB

8.2² = 9.1² + 4.6² - 2(9.1)(4.6) · cosB

67.24 = 82.81 + 21.16 - 83.72 · cosB

-36.73 = -83.72 cosB

0.4387 = cosB

64° = B                                        ∠B in ABCD = 41° + 64° = 105°

c² = b² + d² - 2bd · cosC

9.1² = 8.2² + 4.6² - 2(8.2)(4.6) · cosC

82.81 = 67.24 + 21.16 - 75.44 · cosC

-5.59 = -75.44 cosC

0.074 = cosC

86° = C      

d² = b² + c² - 2bc · cosD

4.6² = 8.2² + 9.1² - 2(8.2)(9.1) · cosD

21.16 = 67.24 + 82.81 - 149.24 · cosD

-128.89 = -149.24 cosD

0.8636 = cosD

30° = D                                        ∠D in ABCD = 84° + 30° = 114°

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Acute angles are those that are less than 90°   --> ∠A & ∠C

Obtuse angles are those that are greater than 90°  --> ∠B & ∠D