Question

If two angles of $\Delta \text{ABC are}{45}^{0}and{60}^0$, then the ratio of the smallest and the greatest sides are

• A.
• B. √3:√2
• C. 1:√3
• D. √3:1

Answer 1

The correct option is A

$\text{Let}A={45}^{0}andB={60}^0\therefore C={75}^0\text{Let smallest and greatest sides are a and c.}\therefore a:c=sin{45}^0:sin{75}^0\frac{1}{\sqrt{2}}:\frac{\sqrt{3}+1}{2\sqrt{2}}=1:\frac{\sqrt{3}+1}{2}=2:\sqrt{3}+1=2(\sqrt{3}-1):2=(\sqrt{3}-1):1$