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Miscellaneous Exercise 3 · Q72

Q.In △ABC\triangle ABC if ∠A=45∘\angle A = 45^\circ, ∠B=30∘\angle B = 30^\circ then a:b:c=a:b:c = _________.

(a) 2:2:3+12 : \sqrt{2} : \sqrt{3}+1
(b) 2:2:3+1\sqrt{2} : 2 : \sqrt{3}+1
(c) 22:2:32\sqrt{2} : \sqrt{2} : \sqrt{3}
(d) 2:22:3+12 : 2\sqrt{2} : \sqrt{3}+1
Maharashtra MsbshseTextbookSubjectiveImportance★★★★★
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C=180∘−45∘−60∘C=180^\circ-45^\circ-60^\circ... using the MCQ's own given angles A=45∘,B=30∘A=45^\circ,B=30^\circ: C=105∘C=105^\circ. sin⁡45∘=12\sin45^\circ=\dfrac{1}{\sqrt2}, sin⁡30∘=12\sin30^\circ=\dfrac12, sin⁡105∘=sin⁡(60∘+45∘)=6+24\sin105^\circ=\sin(60^\circ+45^\circ)=\dfrac{\sqrt6+\sqrt2}{4}. Ratio a:b:c=12:12:6+24a:b:c=\dfrac{1}{\sqrt2}:\dfrac12:\dfrac{\sqrt6+\sqrt2}{4}; multiplying throughout by …

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