Question

ME AJUDEM POR FAVOR↓
Determine a área dos retângulos a seguir, sendo a unidade das medidas metro:

Answer 1

a) Chame a altura de $h$. Pelo Teorema de Pitágoras,

$17^2=h^2+15^2$

$289=h^2+225$

$h^2=64$

$h=8$

$S=bh=15\cdot8=120~\text{m}^2$


b) $\text{tg}~30^{\circ}=\dfrac{h}{12}$

$\dfrac{\sqrt{3}}{3}=\dfrac{h}{12}$

$3h=12\sqrt{3}$

$h=4\sqrt{3}$

$S=bh=12\cdot4\sqrt{3}=48\sqrt{3}~\text{m}^2$.


c) $\text{sen}~60^{\circ}=\dfrac{b}{18}$

$\dfrac{\sqrt{3}}{2}=\dfrac{b}{18}$

$2b=18\sqrt{3}$

$b=9\sqrt{3}$

Pelo Teorema de Pitágoras,

$b^2+h^2=18^2$

$(9\sqrt{3})^2+h^2=324$

$243+h^2=324$

$h^2=81$

$h=9$

$S=bh=9\sqrt{3}\cdot9=81\sqrt{3}~\text{m}^2$.