Question

# Given a right triangle with anglea=23.4^circ. The cathetus opposite to anglea is barA=5.75 m. Find the second cathetus (barB)

Non-right triangles and trigonometry
Given a right triangle with $$\displaystyle\angle{a}={23.4}^{\circ}$$. The cathetus opposite to $$\displaystyle\angle{a}$$ is $$\displaystyle\overline{{A}}={5.75}$$ m. Find the second cathetus $$\displaystyle{\left(\overline{{B}}\right)}$$.

2021-09-01
Since it's a right triangle, use the tanget ratio:
$$\displaystyle{\tan{{\left(\angle\right)}}}=\frac{{\overline{{{o}{p}{p}}}}}{{\overline{{{a}{d}{j}}}}}$$
Substitute values from the given:
$$\displaystyle{{\tan{{23.4}}}^{\circ}=}\frac{{5.75}}{\overline{{B}}}$$
Isolate $$\displaystyle\overline{{B}}$$:
$$\displaystyle\overline{{B}}=\frac{{5.75}}{{{\tan{{23.4}}}^{\circ}}}$$
$$\displaystyle\overline{{B}}\approx{13.29}$$ m