Question

If the angles of a triangle are in ratio 3:4:5 then the sides are in the ratio
(A) 3:4:5
(B) (2)^1/2:(6)^1/2 : (3) ^1/2+1

Answer 1

Hey there!

We know that, Sum of angle in a triangle= 180 °

3x + 4x + 5x = 180

12x = 180

x = 15°

Angles are 45 , 60 , 75 .


According to Law of sines :

a/sinA = b/sinB = c/sinC .

a/sinA = b/sinB.

a/(1/√2 ) = b/ (√3/2)

√2a = 2b/√3

a/b = √2 : √3

a/b = 2 : √6

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b/sin60 = c/sin75

2b/√3 = 2√2c /( √3 + 1 )

b/√3 = √2c / √3 + 1

b /c = √6 / √3 + 1

Now, a : b : c = 2 : √6 : √3 + 1 .

Hope helped!