If any ΔABC , ∠C = 75°, ∠B = 45° and a = √3, then find the value of b.

Concept:

Concept:

In triangle ABC, According to the Sine rule

\(\rm \frac{a}{\text{sin A}}=\frac{b}{\text{sin B}}=\frac{c}{\text{sin C}}\)

Where, a, b, c are sides and A, B, C are angles of triangle.

Sum of the angle in triangle is 180° 

Calculation:

Given: ∠C = 75°, ∠B = 45° and a = √3

∠A + ∠B + ∠C = 180° 

⇒ ∠A = 180° - 75° - 45° 

⇒ ∠A = 60° 

Sine rule

\(\frac{a}{\text{sinA}}=\frac{b}{\text{sinB}}\)

⇒ \(\rm \frac {√3}{sin\ 60^0}\ = \ \frac {b}{sin\ 45^0}\)

⇒ \(\rm \frac {√3}{\frac {√3}{2}}\ = \ \frac {b}{\frac {1}{√2}}\)

⇒ \(\rm b\ = \frac {2}{√2}\)

⇒ b = √2