(a)[3]
find $AM$ expressed in terms of $x$.
(b)[2]
show that the angle is $\theta = \frac{\pi}{6} - \tan^{-1}\left(\frac{1}{2\sqrt{3}}\right)$.
Mathematics 9709 · AS & A Level · Trigonometry
Trigonometry — practice question
From the diagram, triangle $ABC$ is right-angled at $C$, and $M$ is the midpoint of $BC$. You are told that angle $ABC = \frac{\pi}{3}$ radians and angle $BAM = \theta$ radians. If the lengths of $BM$ and $MC$ are each called $x$,
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This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct application of a trigonometric ratio, for example $\tan\left(\frac{\pi}{3}\right)=\frac{AC}{2x}$” …
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