In the triangle $PQR$, $PQ = 3$, $QR= \sqrt{2}$ and angle $PQR= heta +\frac{\pi }{4}$ radians. Give

Question

In the triangle $PQR$, $PQ = 3$, $QR= \sqrt{2}$ and angle $PQR=	heta +\frac{\pi }{4}$ radians. Given that $	heta $ is a sufficiently small angle, show that $PR\approx {{\left( 5+6	heta +3{{	heta }^{2}} ight)}^{\frac{1}{2}}}\approx a+b	heta +c{{	heta }^{2}}$, for constants a, b and c to be determined. [5]

Accepted Answer

$\displaystyle a=\sqrt5$, $\displaystyle b=\frac35\sqrt5$, and $\displaystyle c=\frac3{25}\sqrt5$.

2014 ACJC P1 Q4

2014 ACJC P1 Q4

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