Question

Find the following:

Two complementary angles are in the ratio 3:2.

Answer 1

let the angles be 90-x and the other be x.
given that they are in the ratio of 3:2
so x/90-x = 3/2
2x=270-3x
5x=270
x=54 
as x=54 the other angle would be 90-54 =36

Answer 2

let complementary angles be $\alpha and \beta$
 now, [tex] \alpha + \beta = \pi /2 also, \alpha : \beta =3:2 [/tex]
so, $2 \alpha = 3 \beta$
=> $2 \alpha =3( \pi /2 - \alpha )$
=> $2 \alpha =3 \pi /2 - 3 \alpha$
=> $5 \alpha = 3 \pi /2$
=> $\alpha = 3 \pi /10$ 
  hence, $\alpha = 3 \pi /10 and \beta =2 \pi /10$