Question

find the acute angle between line having slope -1/3 & -2​

Answer 1

The acute angle between the lines having slopes $(-\dfrac{1}{3})$ and $(-2)$ is $45^{\circ}$.

Concept to know :

If $m_{1}$ and $m_{2}$ be the slopes of two intersecting lines, then the angle $\theta$ between the lines is given by

$\quad tan\theta=\dfrac{m_{1}-m_{2}}{1+m_{1}m_{2}}$

where $m_{1}>m_{2}$

Step-by-step explanation :

Given, the slopes of the lines are $(-\dfrac{1}{3})$ and $(-2)$.

Here, $(-\dfrac{1}{3})>(-2)$

Let, $\theta$ be the required angle.

Then, $tan\theta=\dfrac{(-\dfrac{1}{3})-(-2)}{1+(-2)(-\dfrac{1}{3})}$

$\Rightarrow tan\theta=\dfrac{-\dfrac{1}{3}+2}{1+\dfrac{2}{3}}$

$\Rightarrow tan\theta=\dfrac{-1+6}{3+2}$

$\Rightarrow tan\theta=\dfrac{5}{5}$

$\Rightarrow tan\theta=1$

$\Rightarrow \boxed{\theta=45^{\circ}}$