In a triangle ABC right angled at B, AB = 24 cm, BC = 7 cm. then sinC = ?​

Question

In a triangle ABC right angled at B, AB = 24 cm, BC = 7 cm. then sinC = ?​

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Reagan 2 months 2021-12-03T06:43:03+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-12-03T06:44:33+00:00

    Answer:

    In Δ ABC, right-angled at B

    Using Pythagoras theorem

    AC² = AB² +BC²

    AC² = 576 + 49 = 625

    AC = √635

    AC = +25

    Now

    AC = 25 CM, AB = 24cm , BC = 7cm

    sinC=

    side opposite to angle c / hypotenuse =>

    AB / AC => 24/25

    0
    2021-12-03T06:44:45+00:00

    REQUIRED ANSWER : –

    \longrightarrow In ∆ ABC, ∠B = 90°

    \longrightarrow AB = 24 cm BC = 7 cm

    ( by pythyorous therom )

    We have ,

     ac {}^{2}  = ab {}^{2}  +  \: bc {}^{2}

    ac =  \:  \sqrt{(24) {}^{2} }  + (7) {}^{2}

     \sqrt{576 + 49}

     \sqrt{625}

    ➠ AC = 25 cm

    Now , sin A =  \frac{bc}{ac}  =  \frac{7}{25}

    Cos A =  \frac{ab}{ac}  =  \frac{24}{25}

    ANOTHER METHOD IS : –

    ➠ In a given triangle ABC, right-angled at B = ∠B = 90°

    ➠ Given: AB = 24 cm and BC = 7 cm

    ➠ That means, AC = Hypotenuse

    ➠ According to the Pythagoras Theorem,

    ➠In a right-angled triangle, the squares of the hypotenuse side are equal to the sum of the squares of the other two sides.

    ➠ By applying Pythagoras theorem, we get

    ➠ AC2 = AB2 + BC2

    AC2 = (24)2 + 72

    ➠ AC2 = (576 + 49)

    ➠ AC2 = 625 cm2

    ➠ Therefore, AC = 25 cm

    (i) We need to find Sin A and Cos A.

    ➠ As we know, sine of the angle is equal to the ratio of the length of the opposite side and hypotenuse side. Therefore,

    ➠ Sin A = BC/AC = 7/25

    ➠Again, the cosine of an angle is equal to the ratio of the adjacent side and hypotenuse side. Therefore,

    ➠ cos A = AB/AC = 24/25

    (ii) We need to find Sin C and Cos C.

    ➠ Sin C = AB/AC = 24/25

    ➠Cos C = BC/AC = 7/25

    hence proved ,

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