Question

in a triangle ABC , 2A=3B=6C find A

Answer 1

In a triangle, Sum of all three angles is equal to 180°.
Therefore A + B + C = 180°     ------------------(1)
and given that, 2A = 3B = 6C
           ⇒      A = 3C, B = 2C
From eqn (1),
                     A + B +C = 180°
                ⇒ 3C + 2C +C = 180°
                ⇒ 6C = 180°
                ⇒ C = 180/6 = 30°
Therefore A= 3C = 3×30 = 90° and B = 2C = 2×30 = 60°

Answer 2

Given:

• 2A = 3B = 6C

To Find:

• The value of A.

Solution:

It is given that 2A = 3B = 3C.

Let us equate

2A = 6C ⇒ A = 3C → {equation 1}

3B = 6C ⇒ B = 2C → {equation 2}

We did the above step in order to get the values of A and B in terms of C which will be helpful in further calculations.

We know that sum of all angles of a triangle is 180°

⇒ A + B + C = 180°

Now substitute the values of A and b in the above fomula.

⇒ 3C + 2C + C = 180°

⇒ 6C = 180°

⇒ C = 180/6 {dividing the terms}

⇒ C = 30°

By substituting the value of C in equation 2 we will get the value of B.

⇒ B = 2*30 = 60° {multiplying the terms}

Now substitute the value of C in equation 1.

⇒ A = 3*30 = 90° {multipying the terms}

∴ The value of A = 90°