Question

In $\Delta ABC$, if $c=3.4cm,A={25}^{\circ },B={85}^{\circ }$, find a,b and angle C.($sin{25}^o=0.4226,sin{85}^o=0.9962$).

Answer 1

We know that, in a triangle sum of internal angles is ${180}^o$

so, $\angle A+\angle B+\angle C={25}^o+{85}^o+\angle C={180}^o\Rightarrow \angle C={70}^o$

Now, according to sine rule

$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

so, $\frac{a}{\sin A}=\frac{c}{\sin C}\Rightarrow a=c\frac{\sin A}{\sin C}=3.4\ast \frac{\sin {25}^o}{\sin {70}^o}=3.4\ast \frac{0.42}{0.93}=1.535cm$

Similarly ,

$\frac{b}{\sin B}=\frac{a}{\sin A}\Rightarrow b=a\frac{\sin B}{\sin A}=1.53\ast \frac{\sin {85}^o}{\sin {25}^o}=1.53\ast \frac{0.99}{0.42}=3.60cm$