In triangle ABC, AD is perpendicular to BC. sin B = 0.8, BD = 9 cm and tan C =Find:the length of AB, AD, AC and DC.​

Question

In triangle ABC, AD is perpendicular to BC.
sin B = 0.8, BD = 9 cm and tan C =Find:the length of AB, AD, AC and DC.​

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Autumn 1 month 2021-08-14T05:21:06+00:00 1 Answer 0 views 0

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    2021-08-14T05:22:46+00:00

    Answer:

    Sin B = 0.8  

    So cos B = √1-cos² B = √1-(0.8)² = √1-0.64 = √0.36 = 0.6

    In ΔABD,  

    cos B = BD/AB = 0.6 = 9/AB  

    AB = 9/0.6 = 15

    SO AB = 15 cm  

    Sin B = AD/AB

    0.8 = AD/15

    AD = 12 cm

    IN Δ ADC,  

    tan C= AD/CD

    CD = 12 cm  

    and SecC = √1+ tan² C = √1 + 1² = √2

    So,

    SecC = AC/CD  

    = √2 = AC/12

    = AC = 12√2 cm  

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