Question

Find the tangent of the angle between the lines which have intercepts 3, 4 and 1, 8 on the axes respectively.

Answer 1

The respective equations of the lines having intercepts 3, 4 and 1, 8 on the axes are
\[\frac{x}{3} + \frac{y}{4} = 1\]   ... (1) 

\[\frac{x}{1} + \frac{y}{8} = 1\]    ... (2)

Let m₁ and m₂ be the slope of the lines (1) and (2), respectively.

\[\therefore m_1 = - \frac{4}{3}, m_2 = - 8\]

Let \[\theta\] be the angle between the lines (1) and (2).

\[\therefore \tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|\]

\[ = \left| \frac{- \frac{4}{3} + 8}{1 + \frac{32}{3}} \right|\]

\[ \Rightarrow \tan \theta = \frac{4}{7}\]

Hence, the tangent of the angles between the lines is \[\frac{4}{7}\].