Question

In a right-angled triangle, one of the acute angles is 2/3 rd of the other. Find the angles of the triangle.

Answer 1

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-

$A = \dfrac{2}{3}C$

We know that-

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

So, A + B + C = 180

But $A = \dfrac{2}{3}C$

And ∠B = 90°

Then, $\dfrac{2}{3} C + C + 90 = 180$

$\dfrac{2C + 3C}{3} = 180 - 90$

$\dfrac{5C}{3} = 90$

5C = 90×3

5C = 270

$C = \dfrac{270}{5}$

C = 54

Hence, ∠C = 54°

But, $A = \dfrac{2C}{3}$

          $= \dfrac{2 \times54}{3}$

                = 2×18

A = 36

Hence, ∠A = 36°

Answer 2

Answer:

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