In the triangle ABC, the foot of the perpendicular from A to BC is D. Given that tan B =4/3, cos C =15/17 and that AB =20 cm, Calculate without using tables (i) the lengths of sides AC and BC.(ii) the value of sin A.

length of sides AC and BC 
in triangle ABD 
(4x)^2 + (3x)^2 = (20)^2
on solving we get 
x = 4 
similarly  
we get y = 2 
therefore AC = 17 y 
17 * 2 = 34 cm and 
BC = 3x + 15 y = 42 cm 



now to find sin A 
USE FORMULA OF 
SIN A = SIN ( A1 + A2) 
= SIN A1COS A2 + COSA1SINA2  
on solving we get 
sin A = 84/85 
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