Question

Find the acute angle between line having slope 3 and -2.​

Answer 1

The acute angle between line having slope 3 and -2 is 45°

Let us consider the acute angles between the lines to be Ф.

If the two slopes are considered as m and m'.

So, tan Ф = (m - m')/[(1 + mm')]

Here, m = -2 and m' = 3

So, tan Ф = (-2 - 3)/[(1 - 6)] = -5/-5 = 1

Ф = tan⁻¹ (1)

= 45°

This is the subtended angle.

Answer 2

The acute angle between the lines having slopes 3 and -2 is 45° or $\frac{\pi }{4}$.

• Given,

                   $m_{1}=3$, $m_{2}=-2$

• The angle between the lines is given by,

                   $tan\alpha=|\frac{m_{1}-m_{2}}{1+m_{1}m_{2}}|$

                   $tan\alpha=|\frac{3-(-2)}{1+(3)(-2)}|$

                   $tan\alpha=|\frac{5}{1-6}|$

                    $tan\alpha=|\frac{5}{-5}|$

                    $tan\alpha=|-1|$

                    $tan\alpha=$ ± 1

• Since we have to find acute angle between the line, we must take positive value of |-1|.

                    $tan\alpha=1$        

                    $tan\alpha=tan\frac{\pi }{4}$

                        $\alpha=\frac{\pi }{4}$

Therefore, the acute angle between the lines is 45°.