JAMB 1999 · UME · Q29

Find the tangent of the acute angle between the lines $2x + y = 3$ and $3x - 2y = 5$ .

Worked solution (try it first)

Write each line as $y = mx + c$ : $y = -2x + 3$ has $m_1 = -2$ , and $y = \frac32x - \frac52$ has $m_2 = \frac32$ .
The angle between the lines satisfies $\tan\theta = \left|\dfrac{m_1 - m_2}{1 + m_1m_2}\right|$ .
The top is $-2 - \frac32 = -\frac72$ and the bottom is $1 + (-2)\left(\frac32\right) = -2$ .
So $\tan\theta = \frac74$ , option C.