Question

Determine as medidas de x e y em cada item, sabendo que:

Answer 1

a)

$\tan(s) = \frac{x}{1} \\ x = \frac{7}{6}$

${y}^{2} = {1}^{2} + {x}^{2} \\ {y}^{2} = 1 + { (\frac{7}{6} )}^{2} \\ {y}^{2} = 1 + \frac{49}{36}$

${y}^{2} = \frac{85}{36} \\ y = \sqrt{ \frac{85}{36} } \\ y = \frac{ \sqrt{85} }{6}$

b)

$\cos(f) = \frac{3}{x} \\ \frac{3 \sqrt{10} }{10} = \frac{3}{x} \\ \sqrt{10}x = 10$

$x = \frac{10}{ \sqrt{10} } \\ x = \frac{10 \sqrt{10} }{10} \\ x = \sqrt{10}$

${x}^{2} = {y}^{2} + {3}^{2} \\ {( \sqrt{10}) }^{2} = {y}^{2} + 9 \\ {y}^{2} + 9 = 10 \\ {y}^{2} = 10 - 9$

${y}^{2} = 1 \\ y = \sqrt{1} \\ y = 1$

c)

$\cos(b) = \frac{3}{y} \\ \frac{1}{2} = \frac{3}{y} \\ y = 2.3 \\ y = 6$

${y}^{2} = {3}^{2} + {x}^{2} \\ {6}^{2} = {3}^{2} + {x}^{2} \\ {x}^{2} + 9 = 36 \\ {x}^{2} = 36 - 9 \\ {x}^{2} = 27$

$x = \sqrt{27} \\ x = \sqrt{ {3}^{2}.3} \\ x = 3 \sqrt{3}$