Question

Calcule o valor de x em cada triângulo?

Answer 1

a) $\text{sen}~50^{\circ}=\dfrac{2\sqrt{3}}{x}$

$\dfrac{\sqrt{3}}{2}=\dfrac{2\sqrt{3}}{x}$

$\sqrt{3}\cdot x=2\cdot2\sqrt{3}$

$x=\dfrac{4\sqrt{3}}{\sqrt{3}}$

$x=4$

b) $\text{sen}~60^{\circ}=\dfrac{x}{2\sqrt{3}}$

$\dfrac{\sqrt{3}}{2}=\dfrac{x}{2\sqrt{3}}$

$2x=2\sqrt{3}\cdot\sqrt{3}$

$2x=6$

$x=3$

c) $\text{cos}~30^{\circ}=\dfrac{3\sqrt{3}}{x}$

$\dfrac{\sqrt{3}}{2}=\dfrac{3\sqrt{3}}{x}$

$\sqrt{3}\cdot x=2\cdot3\sqrt{3}$

$\sqrt{3}\cdot x=6\sqrt{3}$

$x=\dfrac{6\sqrt{3}}{\sqrt{3}}$

$x=6$

d) $\text{cos}~45^{\circ}=\dfrac{x}{2\sqrt{2}}$

$\dfrac{\sqrt{2}}{2}=\dfrac{x}{2\sqrt{2}}$

$2x=\sqrt{2}\cdot2\sqrt{2}$

$2x=4$

$x=2$

e) $\text{tg}~30^{\circ}=\dfrac{x}{2,5}$

$\dfrac{\sqrt{3}}{3}=\dfrac{x}{2,5}$

$3x=2,5\sqrt{3}$

$x=\dfrac{2,5\sqrt{3}}{3}$

f) $\text{tg}~45^{\circ}=\dfrac{3,8}{x}$

$1=\dfrac{3,8}{x}$

$x=3,8$