Given that
\(Asinθ = 3\)
⇒ \(sinθ = 3/A\) ... (1)
Also,
\(Acosθ = 4\)
⇒ \(cosθ = 4/A\) ... (2)
Squaring (1) and (2), and adding them both we get
\(sin^2θ + cos^2θ = \frac{9}{A^2} + \frac{16}{A^2} = \frac{25}{A^2}\)
⇒ \(1 = \frac{25}{A^2}\)
⇒ \(A = 5\)
Putting Value of \(A\) in (1), we get
\(sinθ = \frac{3}{5} \)
⇒ \(θ = 37°\)