Question

Observe a figura abaixo e determine o valor da área do triângulo OAB...

Answer 1

Explicação passo-a-passo:

$\sf \overline{OB}=cos~\Big(\dfrac{\pi}{3}\Big)$

$\sf \overline{OB}=cos~60^{\circ}$

$\sf \overline{OB}=\dfrac{1}{2}$

• $\sf \overline{OB}=sen~\Big(\dfrac{\pi}{3}\Big)$

$\sf \overline{OB}=sen~60^{\circ}$

$\sf \overline{OB}=\dfrac{\sqrt{3}}{2}$

A área do triângulo OAB é:

$\sf A=\dfrac{b\cdot h}{2}$

$\sf A=\dfrac{\overline{OB}\cdot\overline{OA}}{2}$

$\sf A=\dfrac{\frac{1}{2}\cdot\frac{\sqrt{3}}{2}}{2}$

$\sf A=\dfrac{\frac{\sqrt{3}}{4}}{2}$

$\sf A=\dfrac{\sqrt{3}}{4}\cdot\dfrac{1}{2}$

$\sf \red{A=\dfrac{\sqrt{3}}{8}}$

Letra A