Question

Calcule o valor de x e y nos triângulos retângulos

Answer 1

A) cos45 =$\frac{20}{y}$
$\frac{ \sqrt{2} }{2} = \frac{20}{y}$
$\frac{20 \sqrt{2} }{2y} = \frac{10 \sqrt{2} }{y}$
y = 10$\sqrt{2}$

Sen45 = $\frac{x}{hipotenusa}$
$\frac{ \sqrt{2} }{2} = \frac{x}{10 \sqrt{2} }$
2x = 20
x = $\frac{20}{2}$
x = 10

B) $\frac{1}{2} = \frac{x}{100}$
100 = 2x
x = $\frac{100}{2}$
x = 50

$\frac{ \sqrt{3} }{2} = \frac{y}{50}$
50$\sqrt{3}$ = 2y
y = $\frac{50 \sqrt{3} }{2}$
y = 25$\sqrt{3}$

C) $\frac{ \sqrt{3} }{2} = \frac{2}{x}$
x$\sqrt{3}$ = 4 
x = $\frac{4}{ \sqrt{3} } \frac{ \sqrt{3} }{ \sqrt{3} }$
x = $\frac{4 \sqrt{3} }{3}$

$\frac{1}{2} = \frac{3y}{4 \sqrt{3} }$
6y = 4$\sqrt{3}$
y = $\frac{4 \sqrt{3} }{6}$