Question

Calcule a altura e as projeções dos catetos sobre a hipotenusa no triângulo retângulo de catetos 7cm e 11 cm

Me ajudem por favor

Answer 1

Hipotenusa

$a^2=b^2+c^2 \iff a^2=7^2+11^2 \iff a^2=49+121$

$a^2=170 \iff \boxed{a=\sqrt{170}~\text{cm}}$

Projeções

$b^2=am$

$7^2=\sqrt{170}\cdot m \iff 49=\sqrt{170}\cdot m \iff m=\dfrac{49}{\sqrt{170}}\cdot\dfrac{\sqrt{170}}{\sqrt{170}}$

$\boxed{m=\dfrac{49\sqrt{170}}{170}~\text{cm}}$

$c^2=an$

$11^2=\sqrt{170}\cdot n \iff 121=\sqrt{170}\cdot n \iff n=\dfrac{121}{\sqrt{170}}\cdot\dfrac{\sqrt{170}}{\sqrt{170}}$

$\boxed{n=\dfrac{121\sqrt{170}}{170}~\text{cm}}$