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

Question

Philoid · Accepted Answer

Let a, b, c be the sides of the given triangle. Then by applying the sine rule, we get

Now substituting the given values we get

(∵ sin (a + b) = sin a cos b + sin b cos a)

Now substituting the corresponding values, we get,

Multiplying 2√2, we get

Hence the ratio of the sides of the given triangle is

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