SS2 Math Quiz 10.1 – The cosine rule

In triangle \(ABC\), if \(a = 5\), \(b = 7\), and \(C = 60^\circ\), what is the length of side \(c\)?

6.5

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7.3

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8.1

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5.8

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If \(c = 10\), \(a = 6\), and \(b = 8\), what is the angle \(C\)?

60°

Correct Incorrect Correct answer

45°

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30°

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90°

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What is the cosine rule used for?

To find areas of triangles

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To find angles in right-angled triangles

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To find lengths and angles in non-right-angled triangles

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To calculate perimeter of triangles

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In triangle \(XYZ\), if \(x = 9\), \(y = 12\), and \(Z = 120^\circ\), what is the length of side \(z\)?

8.5

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11.1

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14.4

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15.6

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If the length of sides \(a\) and \(b\) are both 5, and angle \(C\) is \(90^\circ\), what is the length of side \(c\) using the cosine rule?

5

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10

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7.5

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2.5

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In triangle \(ABC\), \(a = 7\), \(b = 10\), and \(C = 45^\circ\). What is \(c\)?

8.9

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10.4

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9.3

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11.2

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Which formula correctly represents the cosine rule?

\(a^2 + b^2 = c^2 + 2ab \cos(C)\)

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\(c^2 = a^2 + b^2 + 2ab \cos(C)\)

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\(c^2 = a^2 + b^2 – 2ab \cos(C)\)

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\(c^2 + a^2 = b^2 – 2ab \cos(C)\)

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If \(a = 3\), \(b = 4\), and \(c = 5\), is triangle \(ABC\) a right triangle?

Yes

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No

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It cannot be determined

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Only if angle \(C\) is 90°

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Find angle \(C\) in triangle \(DEF\) where \(d = 8\), \(e = 6\), and \(f = 10\).

60°

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90°

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30°

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45°

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What is \(C\) if \(c = 8\), \(a = 6\), and \(b = 10\)?

30°

Correct Incorrect Correct answer

60°

Correct Incorrect Correct answer

90°

Correct Incorrect Correct answer

45°

Correct Incorrect Correct answer

SS2 Math Quiz 10.1 – The cosine rule

SS2 Math Quiz 10.1 – The cosine rule

Noah Wasiu September 6, 2024

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