Question

in a right angled tringle one of the acute is 2/3 rd of the other find anglesvof the triangle​

Answer 1

By angle sum property, ∠A+∠B+∠C=180

∘

Given that △ABC is rightangled 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

Answer 2

Answer:

∠A = 36°

∠B = 90°

∠C = 54°

Step-by-step explanation:

According to question-

ABC is a right-angled triangle.

Let ∠B is a right angle. Then-

∠B = 90°

Let, ∠A and ∠C are the two other angles of a triangle.

Given that-

∠A is 2/3rd part of ∠C. Then-

We know that-

The sum of all the angles of a triangle is 180.

So, A + B + C = 180

But

And ∠B = 90°

Then,

5C = 90×3

5C = 270

C = 54

Hence, ∠C = 54°

But,

       

               = 2×18

A = 36

Hence, ∠A = 36 degrees