Question

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Answer 1

Resposta:

a) cos30°=$\frac{10}{x}$

$\frac{\sqrt{3} }{2} = \frac{10}{x}$

$x\sqrt{3} = 20$

$\frac{20}{\sqrt{3} } =\frac{\sqrt{3} }{\sqrt{3} }$

$\frac{20\sqrt{3} }{\sqrt{3} }*\frac{\sqrt{3} }{\sqrt{3} }$

$x = \frac{20\sqrt{3} }{3}$

$a^{2}= b^{2}+ c^{2}$

$(\frac{20\sqrt{3,} }{3}) ^{2} =10^{2} +y^{2}$

400=100+$y^{2}$

$y^{2} =300$

$y=\sqrt{300}$

y=$10\sqrt{3} }cm$

b) cos30°=$\frac{x}{20}$

$\frac{\sqrt{3} }{2} =\frac{x}{20}$

$2x = 20\sqrt{3$

x= $\frac{20\sqrt{3} }{2}$

x= $10\sqrt{3}cm$

$a^{2}= b^{2}+ c^{2}$

$20^{2}= (10\sqrt{3}) ^{2}+ y^{2}$

$400=300+y^{2}$

$y^{2} = 400 - 100$

$y^{2} = 100$

$y =\sqrt{100}$

y=10 cm

c)

cos30° = $\frac{x}{40}$

$\frac{\sqrt{3} }{2}= \frac{x}{40}$

$2x= 40\sqrt{3}$

x= $\frac{40\sqrt{3} }{2}$

x= $20\sqrt{3} cm$

$40^{2}= (20\sqrt{3}) ^{2} +y^{2}$

1600= 1200 +$y^{2}$

$y^{2} = 400$

$y= \sqrt{400}$

y = 20cm

d)

cos30° = $\frac{x}{10}$

$\frac{\sqrt{3} }{2} = \frac{x}{10}$

$2x = 10\sqrt{3}$

x = $5\sqrt{3}  cm$

$10^{2} =(5\sqrt{3} )^{2} +y^{2}$

100 = 75 + $y^{2}$

$y^{2} = 25$

$y = \sqrt{25}$

y = 5

e)

cos30° = $\frac{x}{30}$

$\frac{\sqrt{3} }{2} = \frac{x}{30}$

2x = $30 \sqrt{3}$

x = $\frac{30\sqrt{3} }{2}$

x = $15\sqrt{3} cm$

$30^{2}= (15\sqrt{3} ) ^{2} +y^{2}$

900 = 225 + $y^{2}$

$y^{2} = 675$

y = $\sqrt{675}$

y = 15$\sqrt{3} cm$

f)

cos30° =$\frac{8}{x}$

$\frac{\sqrt{3} }{2} =  \frac{8}{x}$

$\sqrt{3}*x =16$

x= $\frac{16}{\sqrt{3} }$

x= $\frac{16}{\sqrt{16} }= \frac{\sqrt{3} }{\sqrt{3} }$

x= $\frac{16\sqrt{3} }{3}$cm

$(\frac{16\sqrt{3} }{y}) ^{2}= 8^{2} +y^{2}$

256 = 64 + $y^{2}$

$y^{2} = 192$

$y = \sqrt{192}$

y = 8$\sqrt{3} cm$

Explicação passo-a-passo: