Question

determine no triângulo a seguir a medida da hipotenusa a altura em relação a hipotenusa e a projeção dos catetos sobre a hipotenusa .​

Answer 1

Explicação:

• Valor de x

Pelo Teorema de Pitágoras:

$\sf x^2=9^2+16^2$

$\sf x^2=81+256$

$\sf x^2=337$

$\sf \red{x=\sqrt{337}}$

• Valor de h

$\sf a\cdot h=b\cdot c$

$\sf \sqrt{337}\cdot h=9\cdot16$

$\sf \sqrt{337}\cdot h=144$

$\sf h=\dfrac{144}{\sqrt{337}}$

$\sf h=\dfrac{144}{\sqrt{337}}\cdot\dfrac{\sqrt{337}}{\sqrt{337}}$

$\sf \red{h=\dfrac{144\sqrt{337}}{337}}$

• Valor de y

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

$\sf 16^2=\sqrt{337}\cdot y$

$\sf 256=\sqrt{337}\cdot y$

$\sf y=\dfrac{256}{\sqrt{337}}$

$\sf y=\dfrac{256}{\sqrt{337}}\cdot\dfrac{\sqrt{337}}{\sqrt{337}}$

$\sf \red{y=\dfrac{256\sqrt{337}}{337}}$

• Valor de z

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

$\sf 9^2=\sqrt{337}\cdot z$

$\sf 81=\sqrt{337}\cdot z$

$\sf z=\dfrac{81}{\sqrt{337}}$

$\sf z=\dfrac{81}{\sqrt{337}}\cdot\dfrac{\sqrt{337}}{\sqrt{337}}$

$\sf \red{z=\dfrac{81\sqrt{337}}{337}}$