In a ∆ABC, if ∠C
Question:

In a $\triangle A B C$, if $\angle C=\frac{\pi}{2}, \angle A=\frac{\pi}{6}, c=20$, then $a=$_____________________

Solution:

In ∆ABC 

$\angle C=\frac{\pi}{2}, \angle A=\frac{\pi}{6}$

$\Rightarrow \angle B=\frac{\pi}{3}$ (By angle sum property $A+B+C=\pi$ )

using sina formula,

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

$\Rightarrow \frac{a}{\sin \frac{\pi}{6}}=\frac{20}{s \text { in } \frac{\pi}{2}}(\because c=20$ given $)$

 

$\Rightarrow a=\sin \frac{\pi}{6} \times 20(\because \sin \pi / 2=1)$

$\Rightarrow a=\frac{1}{2} \times 20$

 

i.e $a=10$

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