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
ANSWERED
asked 2021-08-31
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 \(\displaystyle{\left(\overline{{B}}\right)}\).

Expert Answers (1)

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
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