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Right triangle with two sides (or their ratio) given: evaluate a ratio expression

This type of question, asked 3 times: 20 Jul 2023 S4, 21 Jul 2023 S4, 11 Sep 2024 S3. All 3 questions below, oldest first.

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  1. Question 1

    20 Jul 2023 S4

    63
    In a right-angle triangle, the hypotenuse is 5 cm and the base is 3 cm. If one angle is θ\theta, then tan⁡θ\tan \theta is equal to:

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  2. Question 2

    21 Jul 2023 S4

    68
    PQR is a triangle right angled at Q and PQ : QR = 3 : 4. What is the value of sin P + sin Q + sin R?

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  3. Question 3

    11 Sep 2024 S3

    74
    Consider a triangle PQR, right angled at R, in which PQ = 29 units, QR = 21 units and ∠PQR=θ\angle PQR = \theta. Find the value of cos⁡2θ−sin⁡2θ\cos^2\theta - \sin^2\theta.

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