Question

a 3. In a right-angled triangle, two acute angles are in a ratio of 2 : 3. Find the measures of the angles.​

Answer 1

Step-by-step explanation:

By angle sum property, ∠A+∠B+∠C=180°

Let the △ABC be right angled at A

∴∠A=90 ∘

∴∠B+∠C=180 ∘

−∠A=180∘ −90∘

=90∘

Given that ∠B:∠C=2:3

Let ∠B=2x and ∠C=3x

⇒2x+3x=90∘

⇒5x=90∘

⇒x= 5

90∘

=18∘

∴∠B=2×18∘

=36∘

and ∠C=3×18∘

=54∘

Hence the other two acute angles are 36°

and 54∘