Question

Determine os valores dos elementos desconhecidos dos ângulos

Answer 1

Resposta:

1)

a)

${6}^{2} = 12x \\ \\ 36 = 12x \\ \\ x = \frac{36}{12} \\ \\ \blue{ x= 3}$

b)

${h}^{2} = 4 \times 16 \\ \\ {h}^{2} = 64 \\ \\ h = \sqrt{64} \\ \\ \blue{h = 8}$

${a}^{2} = {16}^{2} + {8}^{2} \\ \\ {a}^{2} = 256 + 64 \\ \\ {a}^{2} = 320 \\ \\ a = \sqrt{320} \\ \\ a = \sqrt{64 \times 5} \\ \\ a = \sqrt{64} \times \sqrt{5} \\ \\ \blue{a = 8 \sqrt{5} }$

${d}^{2} = {4}^{2} + {8}^{2} \\ \\ {d}^{2} = 16 + 64 \\ \\ {d}^{2} = 80 \\ \\ d = \sqrt{80} \\ \\ d = \sqrt{16 \times 5} \\ \\ d = \sqrt{16} \times \sqrt{5 } \\ \\ \blue{ d = 4 \sqrt{5} }$

c)

${x}^{2} = {6}^{2} + {8}^{2} \\ \\ {x}^{2} = 36 + 64 \\ \\ {x}^{2} = 100 \\ \\ x = \sqrt{100} \\ \\ \blue{x = 10}$

d)

${5}^{2} = {4}^{2} + {x}^{2} \\ \\ 25 = 16 + {x}^{2} \\ \\ 25 - 16 = {x}^{2} \\ \\9 = {x}^{2} \\ \\ {x}^{2} = 9 \\ \\ x = \sqrt{9} \\ \\ \blue{ x = 3}$

Bons Estudos!

Answer 2

Explicação passo-a-passo:

a)

$\sf h^2=m\cdot n$

$\sf 6^2=12\cdot x$

$\sf 6\cdot6=12\cdot x$

$\sf 36=12\cdot x$

$\sf 12\cdot x=36$

$\sf x=\dfrac{36}{12}$

$\large\boxed{\sf \red{x=3}}$

b)

=> Valor de h

$\sf h^2=m\cdot n$

$\sf h^2=4\cdot16$

$\sf h^2=64$

$\sf h=\sqrt{64}$

$\large\boxed{\sf \red{h=8}}$

=> Valor de d

$\sf c^2=a\cdot m$

$\sf d^2=(4+16)\cdot4$

$\sf d^2=20\cdot4$

$\sf d^2=80$

$\sf d=\sqrt{80}$

$\sf d=\sqrt{2^4\cdot5}$

$\sf d=2^2\sqrt{5}$

$\large\boxed{\sf \red{d=4\sqrt{5}}}$

=> Valor de "a"

$\sf b^2=a\cdot n$

$\sf a^2=(4+16)\cdot16$

$\sf a^2=20\cdot16$

$\sf a^2=320$

$\sf a=\sqrt{320}$

$\sf a=\sqrt{2^6\cdot5}$

$\sf a=2^3\sqrt{5}$

$\large\boxed{\sf \red{a=8\sqrt{5}}}$

c)

Pelo Teorema de Pitágoras:

$\sf x^2=6^2+8^2$

$\sf x^2=36+64$

$\sf x^2=100$

$\sf x=\sqrt{100}$

$\sf x=\sqrt{2^2\cdot5^2}$

$\sf x=2\cdot5$

$\large\boxed{\sf \red{x=10}}$

d)

Pelo Teorema de Pitágoras:

$\sf x^2+4^2=5^2$

$\sf x^2+16=25$

$\sf x^2=25-16$

$\sf x^2=9$

$\sf x=\sqrt{9}$

$\sf x=\sqrt{3^2}$

$\large\boxed{\sf \red{x=3}}$