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.​

Answer 1

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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