# Find the Tangent of the Angle Between the Lines Which Have Intercepts 3, 4 and 1, 8 on the Axes Respectively. - Mathematics

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

#### Solution

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 $\frac{4}{7}$.

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.13 | Q 8 | Page 99