Question

Find the value of θ correct to the nearest minute.

Answer 1

$\tan (\angle SPR)=\frac{8.2}{6.5} \longrightarrow \angle SPR=\tan^{-1} \left(\frac{8.2}{6.5} \right)$

$\tan (\angle QPR)=\frac{8.2+5}{6.5} \longrightarrow \angle QPR=\tan^{-1} \left(\frac{8.2+5}{6.5} \right)$$\theta=\angle QPR-\angle SPR=\tan^{-1} \left(\frac{8.2+5}{6.5} \right)-\tan^{-1} \left(\frac{8.2}{6.5} \right)\\\\\theta \approx \boxed{12^{\circ} 11'}$