Question

Find $\tan \theta +\cot \alpha ,\sin \theta ,\cos \alpha$.

Answer 1

$\tan \theta =\frac{BC}{AB}$

$\tan \theta =\frac{15}{20}=\frac{3}{4}$

$\cot \alpha =\frac{BD}{AB}$

$\cot \alpha =\frac{15+6}{20}=\frac{21}{20}$

$\tan \theta +\cot \alpha =\frac{3}{4}+\frac{21}{20}=\frac{9}{5}$

$AD=\sqrt{A{B}^2+B{D}^2}=\sqrt{400+441}=29$

$AC=\sqrt{A{B}^2+B{C}^2}=\sqrt{400+225}=25$

$\therefore \sin \theta =\frac{BC}{AC}=\frac{3}{5}$

$\cos \alpha =\frac{BD}{AD}=\frac{21}{29}$