Question

In $\Delta$ $ABC$ the sides opposite to angles $A,B,C$ are denoted by $a,b,c$ respectively.
In $\Delta$ $ABC$, if $\angle C={90}^0,\angle A={30}^0$ and $c=10$, then the other two sides are:

• A. $a=5,b=5\sqrt{3}$
• B. $a=5\sqrt{3},b=5$
• C. $a=5,b=5$
• D. $a=5\sqrt{3},b=5\sqrt{3}$

Answer 1

Answer: (A)

$a=5,b=5\sqrt{3}$

$\frac{a}{\sin {30}^o}=\frac{10}{\sin {90}^o}\Rightarrow a=5$

$A+B+C={180}^{o}B={180}^o-{90}^o-{30}^o={60}^o$

$\frac{b}{\sin {60}^o}=\frac{10}{1}\Rightarrow b=5\sqrt{3}$

Therefore Answer is $A$