1.

If the angles of a triangle are in the ratio 1 : 2 : 3, prove that its corresponding sides are in the ratio 1:√3:2.

Answer»

Given: Angles of a triangle are in the ratio 1 : 2 : 3

To prove: Its corresponding sides are in the ratio 1:√3:2

Let the angles are x , 2x , 3x 

Therefore, x + 2x + 3x = 180°

6x = 180°

x = 30°.

So, the angles are 30°. , 60°. , 90°

So, the ratio of the corresponding sides are: 

= sin30°. : sin60°. : sin90°.

= 1/2: √3/2:1

= 1:√3:2 [proved]



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