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If the angle of triangles are in the ratio 2:3:7, then the sides are in ratio of? PLS EXPLAIN!!!!!!

If the angle of triangles are in the ratio 2:3:7, then the sides are in ratio of?


PLS EXPLAIN!!!!!!

Grade:9

2 Answers

shaswat roy
19 Points
10 years ago

the ratio of the angles are given, therefore by using the fact that sum of three angles  is 180 deg, you will get the 3 angles of the triangle which are 30deg,45deg,105deg. find the sine of these angles and then simply use sine rule.

himanshu panwar
30 Points
10 years ago

Let a,b,c be the sides and A,B,C be the angles of a triangle

Given  A:B:C =2:3:7

A=2x ; B=3x ; C=7x ;

A+B+C =180  or

2x+3x+7x =180 

then x=15

or

A=30° ; B=45° ; C=105° ;

By sine rule 

a:b:c = sineA : sineB : sineC

a:b:c = sine30 : sine45 : sine(60+45)

       =1/2 : 1/√2 : ( √3/2√2 + 1/2√2 )

 

hence a : b : c  =  √2 : 2 : (√3 + 1)

 

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