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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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