Question

# A right triangle has a cathetus of 75m, which is opposite to the anfle of 40'. Find the adjustent cathetus to the 40' angle.

Non-right triangles and trigonometry
A right triangle has a cathetus of 75m, which is opposite to the anfle of 40'. Find the adjustent cathetus to the 40' angle.

2021-09-11
$$\displaystyle{40}'=\frac{{40}}{{60}^{\circ}}$$
$$\displaystyle=\frac{{2}}{{3}^{\circ}}$$
Use the tangent ratio:
$$\displaystyle{\tan{\angle}}=\frac{{{o}{p}{p}}}{{{a}{d}{j}}}$$
Let the adj. side be x. Substitute the given:
$$\displaystyle{{\tan{{\left(\frac{{2}}{{3}}\right)}}}^{\circ}=}\frac{{75}}{{x}}$$
$$\displaystyle{x}=\frac{{75}}{{{\tan{{\left(\frac{{2}}{{3}}\right)}}}^{\circ}}}$$
$$\displaystyle{x}\approx{6445.5}{m}$$