Question

In tri. ABC , right angled at B , AB = 5cm and sinC = 1/2 . Determine the lenght of side AC.

Answer 1

Given: <B = 90° and AB = 5cm, SinC = 1/2

=> SinC = $\rm\frac{1}{2}$

=> SinC = Sin30°

=> C = 30°

<A + <B + <C = 180° {angle sum property}

=> <A + 90° + 30° = 180°

=> <A = 180° - 120°

=> <A = 60°

CosA = $\rm\frac{AB}{AC}$

=> Cos60° = $\rm\frac{5}{AC}$

=> $\rm\frac{1}{2} = \frac{5}{AC}$

=> AC = 10cm

So, the length of side AC is 10cm