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The anglesbof a triangle are in the ratio 11 : 5 : 2. The side opposite the largest angle is 5.5 centimeters. The length of the side opposite the smallest angle of the triangle is

User Exexzian
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The largest side is opposite the largest angle, the smallest side is opposite the smallest angle. 11+5+2=18, and 180/18=10, so the angles are



A=110^\circ, B=50^\circ, C=20^\circ


The longest side is opposite the largest angle, so



a = 5.5 \textrm{ cm}


The shortest side is opposite the smallest angle, so
c.


The Law of Sines says



(c)/(\sin C)=(a)/(\sin A)



c=(a \sin C)/(\sin A)



c=(5.5 \sin 20^\circ)/(\sin 110^\circ) \approx 2.00184


Answer (rounded): 2.00



User Tresa
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