The diagram shows triangle $ABC$, where angle $ACD=\left( \frac{\pi }{4}+x \right)$ radians. Poi

Question

The diagram shows triangle $ABC$, where angle $ACD=\left( \frac{\pi }{4}+x \right)$ radians. Point $D$ is on $BC$ such that $AD=2$ and $BD=2\sqrt{3}$. Show that if $x$ is sufficiently small for ${{x}^{3}}$ and higher powers of $x$ to be neglected, then $BC\approx k\left( 1+\sqrt{3}-2x+2{{x}^{2}} \right)$, where $k$ is a constant to be determined.[5]

Accepted Answer

$ \therefore k=2$

2022 VJC P1 Q2

2022 VJC P1 Q2

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