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Sed (CoderLovesEggs) Paper 1 with Solutions · Q17

Paper 1TrigonometryGeometryFunctions & graphs

In triangle ABCABC,

  • ∠BAC=30∘\angle BAC=30^\circ;
  • AC=12AC=12;
  • 67<sin⁡(∠ABC)≤1\dfrac67<\sin(\angle ABC)\le1.

Denote SS as the area of ABCABC. It follows that the range of SS is:

A183−3132<S<183+313218\sqrt3-\dfrac{3\sqrt{13}}2<S<18\sqrt3+\dfrac{3\sqrt{13}}2;
B183−313<S<183+31318\sqrt3-3\sqrt{13}<S<18\sqrt3+3\sqrt{13};
C0<S<183+9130<S<18\sqrt3+9\sqrt{13};
D183<S<183+31318\sqrt3<S<18\sqrt3+3\sqrt{13};
E183−3613<S<183+361318\sqrt3-\dfrac{36}{\sqrt{13}}<S<18\sqrt3+\dfrac{36}{\sqrt{13}}.

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