Question

in ∆ abc, 2A=3B,5B=2C. determine the angles of triangle​

Answer 1

Answer:

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

Answer:

Required value of three angles A,B,C are 36°,54° and 90° respectively

Step-by-step explanation:

Given,2A=3B,5B=2C

Now,

$2A = 3B \\ A = \frac{3B}{2} .....(1)$

and

$5B = 2C \\ C = \frac{5B}{2} .....(2)$

We know,sum of all angles of a triangle $= {180}^{o}$

Therefore,

$A + B + C = {180}^{o}$

Now we are putting value of A and C,

$\frac{3B}{2} + B + \frac{5B}{2} = {180}^{o} \\ \frac{3B + 2B + 5B}{2} = {180}^{o} \\ \frac{10B}{2} = {180}^{o} \\ B = \frac{ {180}^{o} }{5} \\ B = {36}^{o}$

From equation (1),

$A = \frac{3B}{2} \\ = \frac{3 \times {36}^{o} }{2} \\ = 3 \times {18}^{o} \\ = {54}^{o}$

and

$C = \frac{5B}{2} \\ = \frac{5 \times {36}^{o} }{2} \\ = 5 \times {18}^{o} \\ = {90}^{o}$

Therefore, required value of three angles A,B,C are 36°,54° and 90° respectively.

This is a angle related problem.

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