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

`(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