Question

$\Delta$ABC is right-angled at $\angle$A. Find $\tan ,\sin$ and $\cos$ of angles B and C in the following case. AB$=12$cm, AC$=9$cm.

Answer 1

$\begin{array}{c}BypythagoroustheoremA{C}^2+A{B}^2=B{C}^{{}^2}\\ 9^2+{12}^2=B{C}^2\\ 81+144=B{C}^2\\ \sqrt{225}=BC\\ \therefore BC=15cm\\ \sin B=\frac{9}{15}\\ \cos B=\frac{12}{15}\\ \tan B=\frac{9}{12}\\ \sin C=\frac{12}{15}\\ \cos C=\frac{9}{15}\\ \tan C=\frac{12}{9}\end{array}$