2022 HCI P1 Q2
In the figure below, $ABC$ is an equilateral triangle of length $2k$ units while $ABD$ is a triangle where $AD$ is of length $k$ units and $\measuredangle CAD$ is $x$ radians.
(i)
Show that $B{{D}^{2}}={{k}^{2}}\left( 5-2\cos x+2\sqrt{3}\sin x \right)$.
[2]
(ii)
Given that $x$ is sufficiently small such that ${{x}^{3}}$ and higher powers of $x$ may be may be neglected, find an approximation in $x$ for the length $BD$, leaving your answers in exact form and in terms of $k$.
[4]
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