Question

In a ∆ABC, if 2angle equals to 3 angle b equal to 6 angle c calculate angle a angle b and angle c
​

Answer 1

Answer:

a=90°, b=60° and c=30°

Explanation:

2a=3b=6c

(i) a = 3b/2

(ii) c = 3b/6 = b/2

SO, In ΔABC

⇒ a + b + c=180°

or, 3b/2 + b + b/2= 180°     [∵From EQn (i) and (ii)]

or, 3b + 2b + b = 180° × 2   [∵Taking LCM on LHS and taking 2 to the RHS]

or, 6b = 360°

∴ b = 60°

⇒ a = 3b/2 = (3×60°)/2 = 90°

⇒ c = b/2 = 60°/2 = 30°

Thus,

In ΔABC, ∡a = 90°

               ∡b = 60°

               ∡c = 30°