Question

determine a inclinação da reta A(2;3) e B(4;9)​

Answer 1

✅ Após resolver os cálculos, concluímos que a medida aproximada do ângulo de inclinação da referida reta no plano cartesiano é:

      $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf \theta \cong 71,56^{\circ}\:\:\:}}\end{gathered} }$

Sejam os pontos:

             $\Large\begin{cases} A = (2, 3)\\B = (4, 9)\end{cases}$

Sabemos que o ângulo de inclinação de uma reta no plano cartesiano é numericamente igual à medida do arco cuja tangente vale o coeficiente angular da reta, ou seja:

          $\Large\displaystyle\begin{gathered} \theta = \arctan(m_{r})\end{gathered}$

              $\Large\displaystyle\begin{gathered} = \arctan(\tan\theta)\end{gathered}$

              $\Large\displaystyle\begin{gathered} = \arctan\bigg(\frac{\sin\theta}{\cos\theta}\bigg)\end{gathered}$

              $\Large\displaystyle\text{ \begin{gathered} = \arctan\bigg(\frac{y_{B} - y_{A}}{x_{B} - x_{A}}\bigg)\end{gathered} }$

              $\Large\displaystyle\begin{gathered} = \arctan\bigg(\frac{9 - 3}{4 - 2}\bigg)\end{gathered}$

               $\Large\displaystyle\begin{gathered} = \arctan\bigg(\frac{6}{2}\bigg)\end{gathered}$

               $\Large\displaystyle\begin{gathered} = \arctan(3)\end{gathered}$

               $\Large\displaystyle\begin{gathered} \cong 71,56^{\circ}\end{gathered}$

✅ Portanto, o ângulo de inclinação é:

           $\Large\displaystyle\begin{gathered} \theta \cong 71,56^{\circ}\end{gathered}$

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

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