If two angles of $ riangle A B C$ are $45^{\circ}$ and $60^{\circ}$, then the ratio of the smallest and the greatest sides are

Question

If two angles of $	riangle A B C$ are $45^{\circ}$ and $60^{\circ}$, then the ratio of the smallest and the greatest sides are

Aicharya · Accepted Answer

Let $A=45^{\circ}$ and $B=60^{\circ}$ $	herefore \quad C=75^{\circ}$ Let smallest and greatest sides are $a$ and $c$. $	herefore \quad \begin{aligned} a: c & =\sin 45^{\circ}: \sin 75^{\circ} \ & =\frac{1}{\sqrt{2}}: \frac{\sqrt{3}+1}{2 \sqrt{2}} \ & =1: \frac{\sqrt{3}+1}{2} \ & =2: \sqrt{3}+1 \ & =1: \sqrt{3}\end{aligned}$

If two angles of $\triangle A B C$ are $45^{\circ}$ and $60^{\circ}$, then the ratio of the smallest and the…

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