Question

calcule o valor de x e y nos triangulos retangulos.

Answer 1

Resposta:

a) $x=20$ e $y=20\sqrt{2}$

b) $x=50\sqrt{3}$ e $y=50$

c) $x=4$ e $y=2\sqrt{3}$

Explicação passo-a-passo:

a) $\text{tg}~45{\circ}=\dfrac{x}{20}$

$1=\dfrac{x}{20}~\Rightarrow~\boxed{x=20}$

$\text{sen}~45^{\circ}=\dfrac{x}{y}$

$\dfrac{\sqrt{2}}{2}=\dfrac{20}{y}$

$\sqrt{2}\cdot y=40$

$y=\dfrac{40}{\sqrt{2}}=\dfrac{40\sqr{2}}{2}~\Rightarrow~\boxed{y=20\sqrt{2}}$

b) $\text{sen}~60^{\circ}=\dfrac{x}{100}$

$\dfrac{\sqrt{3}}{2}=\dfrac{x}{100}$

$2x=100\sqrt{3}~\Rightarrow~\boxed{x=50\sqrt{3}}$

$\text{cos}~60^{\circ}=\dfrac{y}{100}$

$\dfrac{1}{2}=\dfrac{y}{100}$

$2y=100~\Rightarro~\boxed{y=50}$

c) $\text{sen}~30^{\circ}=\dfrac{2}{x}$

$\dfrac{1}{2}=\dfrac{2}{x}~\Rightarrow~\boxed{x=4}$

$\text{tg}~30^{\circ}=\dfrac{2}{y}$

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

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

$y=\dfrac{6}{\sqrt{3}}=\dfrac{6\sqrt{3}}{3}~\Rightarrow~\boxed{y=2\sqrt{3}}$