Question

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

Answer 1

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

$\dfrac{c}{\sin C}=\dfrac{a}{\sin A}$

$c=\dfrac{a \sin C}{\sin A}$

$c=\dfrac{5.5 \sin 20^\circ}{\sin 110^\circ} \approx 2.00184$

Answer (rounded): 2.00