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Largest or smallest angle from the three sides by the cosine rule

This type of question, asked 5 times: 2 May 2023 S2, 9 May 2023 S1, 11 May 2023 S1, 19 Apr 2025 S1, 20 Apr 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    2 May 2023 S2

    133
    If the lengths of the sides of a triangle are 3,5,73, 5, 7, then the largest angle of the triangle is

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  2. Question 2

    9 May 2023 S1

    114
    The sides of a triangle are sin⁡θ\sin\theta, cos⁡θ\cos\theta and 1+sin⁡θcos⁡θ\sqrt{1+\sin\theta\cos\theta} for some 0<θ<π20<\theta<\frac{\pi}{2}, then the greatest angle of a triangle is

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  3. Question 3

    11 May 2023 S1

    140
    With usual notations, if the lengths of the sides of a triangle are 7 cm, 434\sqrt{3} cm and 13\sqrt{13} cm, then the measures of the smallest angle is

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  4. Question 4

    19 Apr 2025 S1

    147
    The smallest angle of the triangle whose sides are 6+12,48,246 +\sqrt{12},\sqrt{48},\sqrt{24} is

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  5. Question 5

    20 Apr 2026 S2

    63
    With the usual notations, if the lengths of the sides of the triangle are 3 units, 5 units and 7 units, then the largest angle of the triangle is

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