The perimeter of a triangle is 100cm and the angles are in the ratio of 1:3:5. Find the length of each side.

\(\displaystyle x+3x+5x= 180\)

\(\displaystyle x = 20\)

angles are 20,60,100

Now use these formulas

\(\displaystyle \frac{\sin{60}}{a} = \frac{\sin{20}}{b} = \frac{\sin{100}}{c}\)

\(\displaystyle a + b + c = 100\)

Now solve for a variable and sub

\(\displaystyle a = \frac{b\sin{60}}{\sin{20}}\)

\(\displaystyle c = \frac{b\sin{100}}{\sin{20}}\)

so now sub

\(\displaystyle \frac{b\sin{60}}{\sin{20}} + b + \frac{b\sin{100}}{\sin{20}} = 100\)