Question

O coeficiente angular da reta que tem inclinação de 30° é ?

Answer 1

Vamos lá

O coeficiente angular da reta que tem inclinação de 30° é

a = tg(30) = √3/3

Answer 2

✅ Após resolver os cálculos, concluímos que o coeficiente angular da referida reta é:

  $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf m_{r} = \frac{\sqrt{3}}{3}\:\:\:}}\end{gathered} }$

Seja o ângulo de inclinação:

             $\Large\displaystyle\begin{gathered} \theta = 30^{\circ}\end{gathered}$

Sabemos que o coeficiente angular de qualquer reta no plano cartesiano  é numericamente igual à tangente do ângulo de inclinação da referida reta, ou seja:

$\Large\displaystyle\begin{gathered} \bf I\end{gathered}$         $\Large\displaystyle\begin{gathered} m_{r} = \tan\theta\end{gathered}$

Substituindo o ângulo na equação "I", temos:

          $\Large\displaystyle\begin{gathered} m_{r} = \tan30^{\circ}\end{gathered}$

                  $\Large\displaystyle\text{ \begin{gathered} = \frac{\sin30^{\circ}}{\cos30^{\circ}}\end{gathered} }$

                  $\Large\displaystyle\text{ \begin{gathered} = \frac{\dfrac{1}{2}}{\dfrac{\sqrt{3}}{2}}\end{gathered} }$

                   $\Large\displaystyle\text{ \begin{gathered} = \frac{1}{\!\diagup\!\!\!\!2}\cdot\frac{\!\diagup\!\!\!\!2}{\sqrt{3}}\end{gathered} }$

                   $\Large\displaystyle\text{ \begin{gathered} = \frac{1}{\sqrt{3}}\end{gathered} }$

                   $\Large\displaystyle\text{ \begin{gathered} = \frac{1}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}\end{gathered} }$

                   $\Large\displaystyle\text{ \begin{gathered} = \frac{\sqrt{3}}{(\sqrt[\!\diagup\!]{3})^{\!\diagup\!\!\!\!2}}\end{gathered} }$

                   $\Large\displaystyle\text{ \begin{gathered} = \frac{\sqrt{3}}{3}\end{gathered} }$

✅ Portanto, o coeficiente angular procurado é:

            $\Large\displaystyle\text{ \begin{gathered} m_{r} = \frac{\sqrt{3}}{3}\end{gathered} }$

$\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered} }$

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