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Activity Discussion Math trigonometry

  • trigonometry

    Posted by Geethika on June 24, 2023 at 9:12 pm

    In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm.

    Determine:
    (i) sin A, cos A
    (ii) sin C, cos C

    Harshwardhan replied 5 months, 1 week ago 3 Members · 2 Replies
  • 2 Replies
  • Akshar

    Member
    December 3, 2023 at 12:51 pm
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    ::

    As given in question, In triangle ∆ABC. AB = 24 and BC = 7.

    So the value of Hypotenuse (AC) would be 25.

    Sin A = 7/25 = 0.28

    Cos A = 24/25 = 0.96

    Sin C = 24/25 = 0.96

    Cos C = 7/25 = 0.28

  • Harshwardhan

    Member
    December 15, 2023 at 2:27 pm
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    ::

    To find the values of sin A, cos A, sin C, and cos C in triangle ABC, we can use the following trigonometric ratios:

    • sin A = opposite side / hypotenuse = BC / AC

    • cos A = adjacent side / hypotenuse = AB / AC

    • sin C = opposite side / hypotenuse = AB / AC

    • cos C = adjacent side / hypotenuse = BC / AC

    We are given that AB = 24 cm and BC = 7 cm. We need to find AC first, which is the hypotenuse of the triangle. We

    can use the Pythagorean theorem to do this:

    ACA2 = ABA2 + BCA2

    ACA2 = 24A2 + 7A2

    ACA2 = 625

    AC = 4625

    AC = 25 cm

    Now that we know all the side lengths of the triangle, we can find the values of the trigonometric ratios:

    sin A

    sin C

    = BC/AC=7 /25

    = 24 / 25 (Note: sin C is the same as sin A because angle C is the complement of angle A)

    = AB/AC

    Therefore, the values of sin A, cos A, sin C, and cos C are 7/25, 24/25, 24/25, and 7/25, respectively.

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