Question

If in a ∆ABC, ∠A = 45°, ∠B = 60°, and ∠C = 75°; find the ratio of its sides.

Answer 1

Given as in ∆ABC, ∠A = 45°, ∠B = 60°, and ∠C = 75°

On using the sine rule, 

a/sin A = b/sin B = c/sin C

On substituting the values 

As we know that, sin(a + b) = sin a cos b + sin b cos a

On substituting the corresponding values,

Then, multiply the above expression by 2√2,

a: b: c = 2: √6:(1 + √3)

Thus the ratio of the sides of the given triangle is a: b: c = 2: √6:(1 + √3)