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Juan Set 1 Paper 1 · Q21

Paper 1TrigonometryGeometry

Bonus question. Let a triangle ABCABC have side lengths ∣BC∣=a|BC|=a units, ∣AC∣=b|AC|=b units, and ∣AB∣=c|AB|=c units, satisfying

2a2=2b2+2c2+3bc.2a^2=2b^2+2c^2+3bc.

Given that xx is the size of angle BACBAC, what is the value of tan⁡x\tan x?

A−23-\dfrac{\sqrt{2}}{3}
B−33-\dfrac{\sqrt{3}}{3}
C−53-\dfrac{\sqrt{5}}{3}
D−63-\dfrac{\sqrt{6}}{3}
E−73-\dfrac{\sqrt{7}}{3}

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