Question

A Hipotenusa de um triângulo retângulo vale 70 m, e um dos ângulos vale 30º. Qual
a área do triângulo?

Answer 1

$\text{Hipotenusa}\ \to\ a=70\ m\\\\ \text{Cateto 1}\ (b)\ \to\ \sin{30}=\dfrac{b}{a}\ \therefore\ \dfrac{1}{2}=\dfrac{b}{70}\ \therefore\ b=35\ m\\\\ \text{Cateto 2}\ (c)\ \to\ \cos{30}=\dfrac{c}{a}\ \therefore\ \dfrac{\sqrt{3}}{2}=\dfrac{c}{70}\ \therefore\ c=35\sqrt{3}\ m$

$\mathrm{\acute{A}rea}\ (S)\ \to\ S=\dfrac{bc}{2}=\dfrac{35(35\sqrt{3})}{2}\ \therefore\ \boxed{S=\dfrac{1225\sqrt{3}}{2}\ m^2}$

$\boxed{S\approx1060.88\ m^2}$