Find the ratio of the sides of a triangle if:
(a) the angles are in the ratio 1:2:3
(b) the angles are in the ratio 4:5:6
Hi sinjid9,
if the ratio of angles is 1:2:3 there are 6 parts and the sum of the angles in a triangle is 180 degrees.
One angle is \(\displaystyle \frac{180^o}{6}=30^o\)
The other angles are twice and three times that, \(\displaystyle 60^o,\ 90^o\)
To calculate the ratios of the sides, you can re-arrange the Sine Rule (Law of Sines).
\(\displaystyle \frac{SinA}{a}=\frac{SinB}{b}=\frac{SinC}{c}\)
to get
\(\displaystyle \frac{SinA}{SinB}=\frac{a}{b}\)
then a:b=SinA:SinB
Also \(\displaystyle \frac{SinB}{b}=\frac{SinC}{c}\)
\(\displaystyle \frac{SinB}{SinC}=\frac{b}{c}\)
then a:b:c=SinA:SinB:SinC
When the ratio of the angles is 4:5:6, there are 15 parts
\(\displaystyle \frac{180^o}{15}=12^o\)
Then the angles are \(\displaystyle 4(12^o),\ 5(12^o),\ 6(12^o)\)
then solve as above