Question

In $△PQR$, $\frac{PQ}{1}=\frac{PR}{2}=\frac{QR}{\sqrt{3}}$, then $m\angle R\left(indegrees\right)=........$

• A. $90$
• B. $60$
• C. $45$
• D. $30$

Answer 1

The correct option is A $90$

Let us assume $\frac{PQ}{1}=\frac{PR}{2}=\frac{QR}{\sqrt{3}}=k$,

Then $PQ=k,QR=2k$ and $PR=$$\sqrt{3}$$k$ respectively.

Thus, $\cos R=\frac{{PR}^2+{QR}^2-{PQ}^2}{2.PR.QR}$

$=\frac{(2k{)}^2+(\sqrt{3}{)}^2-k^2}{2.\left(\sqrt{3}k\right).\left(2k\right)}$

$=\frac{6}{4\sqrt{3}}$

$=\frac{\sqrt{3}}{2}$

Therefore, m$\angle R=30$