Question

Find the ratio of the sides of a triangle whose interior angles are ${30}^o,{60}^{o}and{90}^o$ degrees?

• A. $1$ : $\frac{1}{\sqrt{3}}$: $\frac{1}{2}$
• B. $1$ :$2$: $2$
• C. $1$ : $2$ : $3$
• D. $1$ : $3$ : $1$

Answer 1

Answer: (A)

$1$ : $\frac{1}{\sqrt{3}}$: $\frac{1}{2}$

sine rule of triangle
$\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}$
$\Rightarrow$ Given interior angles are ${30}^o,{60}^0$ and ${90}^o$
$\therefore \frac{sin{30}^o}{a}=\frac{sin{60}^o}{b}=\frac{sin{90}^o}{c}$
$\Rightarrow 2a=\frac{2b}{\sqrt{3}}=c$
$\Rightarrow 2\sqrt{3}a=2b=\sqrt{3}c$
$\Rightarrow a=\frac{b}{\sqrt{3}}=\frac{c}{2}$
$\Rightarrow 1:\frac{1}{\sqrt{3}}:\frac{1}{2}$