If in any ∆ABC, ∠ C = 105 o , ∠ B = 45 o , a = 2, then find b.

Question

Philoid · Accepted Answer

We know in a triangle,

∠A + ∠B + ∠C = 180°

⇒ ∠A = 180° - ∠B - ∠C

Substituting the given values, we get

∠A = 180° - 45° - 105°

⇒ ∠A = 30°

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

Now substituting the corresponding values we get

Substitute the equivalent values of the sine, we get

Hence the value of b is 2√2 units.

If in any ∆ABC, ∠C = 105o, ∠B = 45o, a = 2, then find b.