Question

Prove that the sum of angles of a triangle is two right angles .if angles of a triangle are the ratio 3:4:5, find the smallest angle .

Answer 1

Let the three angles be 3x,4x,5x3x,4x,5x degrees then

3x+4x+5x=180∘3x+4x+5x=180∘

12x=180∘12x=180∘

x=180∘12x=180∘12

x=15∘x=15∘

Smallest angle =3x3x

=3×15∘=3×15∘

=45∘=45∘

Greatest angle =5x5x

=5×15∘=5×15∘

=75∘=75∘

In radian ⇒75∘×π180∘⇒75∘×π180∘

⇒5π12⇒5π12 radians.