Question

Calcule o valor dos elementos desconhecidos nós triângulos retângulos.
Me ajudem por favooor

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm Relac_{\!\!,}\tilde oes~M\acute etricas}\\\rm\underline{No~tri\hat angulo~Ret\hat angulo}\\\sf 1\cdot~\green{b^2}=\blue{m}\cdot\orange{ n}\\\sf 2\cdot~\red{c^2}=\blue{a}\cdot\pink{n}\\\sf 3\cdot~h^2=\orange{m}\cdot\pink{n}\\\sf 4\cdot~\blue{a}\cdot h=\green{b}\cdot\red{c}\\\sf 5\cdot~\blue{a^2}=\green{b^2}+\red{c^2}\end{array}}$

$\boxed{\begin{array}{l}\tt a)~\sf usando~a~relac_{\!\!,}\tilde ao~1~temos:\\\sf x^2=25\cdot9\\\sf x=\sqrt{25\cdot9}\\\sf x=5\cdot3=15\\\tt b)~\sf usando~a~relac_{\!\!,}\tilde ao~2~temos\\\sf x^2=9\cdot5\\\sf x=\sqrt{9\cdot5}\\\sf x=3\sqrt{5}\\\tt c)~\sf usando~a~relac_{\!\!,}\tilde ao~4~temos\\\sf5 \cdot h=3\cdot4\\\sf h=\dfrac{12}{5}\\\tt d)~\sf usando~a~relac_{\!\!,}\tilde ao~3~temos \\\sf h^2=4\cdot16\\\sf h=\sqrt{4\cdot16}\\\sf h=2\cdot8=16\end{array}}$

$\boxed{\begin{array}{l}\tt e)~\sf usando~a~relac_{\!\!,}\tilde ao~1~temos:\\\sf x^2=20\cdot16\\\sf x^2=5\cdot4\cdot16\\\sf x=\sqrt{5\cdot4\cdot16}\\\sf x=2\cdot4\sqrt{5}=8\sqrt{5}\\\tt f)~\sf usando~a~relac_{\!\!,}\tilde ao~ 3~temos:\\\sf 12^2=h\cdot16\\\sf 16h=144\\\sf h=\dfrac{144}{16}\\\sf h=9\end{array}}$