Question

62) If the ratio of angles of a
triangle is 3:4:5, then is ratio of its
sides is ....​

Answer 1

the ratio of sides are 2:√6:√3+1

Step-by-step explanation:

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

____________________________________________

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!