Question

If the angles of a triangle are in the ratio 1 : 2 : 3, then their

corresponding sides are in the ratio

• A. 1 : 2 : 3
• B. 1 : $\sqrt { 3 }$: 2
• C. $\sqrt { 2 }$: $\sqrt { 3 }$: 3
• D. 1 :$\sqrt { 3 }$: 3

Answer 1

Answer: (B)

1 : $\sqrt { 3 }$: 2

Answer 2

A : B : C = 1 : 2 : 3

Let the angles are x, 2x and 3x

∴ x + 2x + 3x = 180⁰ ⇒ x = 30⁰

∴ angles are 30⁰, 60⁰, 90⁰

a : b : c = k sin A : k sin B : k sin C

= sin 30⁰ : sin 60⁰ : sin 90⁰

= $\frac { 1 } { 2 }$: $\frac { \sqrt { 3 } } { 2 }$ : 1= 1 : $\sqrt { 3 }$: 2