Exercises: Sine, Cosine and Tangent on a right triangle

This sketch shows a right triangle, not true to size, with height $h=8\mathrm{cm}$ and angles $\mathrm{\alpha }={65}^{\circ }$ and $\beta ={80}^{\circ }$.

Calculate the side lengths $a$ and $b$.

$\begin{array}{l}a=\tan \left(\alpha \right)\cdot h\\ a=\tan \left({65}^{\circ }\right)\cdot 8\mathrm{cm}\\ a=17.16\mathrm{cm}\\ \\ b=\tan \left(\beta \right)\cdot h\\ b=\tan \left({80}^{\circ }\right)\cdot 8\mathrm{cm}\\ b=45.37\mathrm{cm}\end{array}$