Question

Calculate, correct to one decimal plice

Answer 1

Answer:

A. 70.69 is the correct answer.

Step-by-step explanation:

Given:

Two lines:

$3x - 4y + 5 = 0 \\2x + 3y -1 = 0$

To find:

Angle between the two lines = ?

Solution:

Acute Angle between two lines can be found by using the below formula:

$tan \theta = |\dfrac{(m_1 - m_2)}{ (1 + m_1m_2)}|$

Where $\theta$ is the acute angle between two lines.

$m_1, m_2$ are the slopes of two lines.

Slope of a line represented by $ax+by+c=0$ is given as:

$m = -\dfrac{a}{b }$

So,

$m_1 = -\dfrac{3}{- 4} = \dfrac{3}{4}$

$m_2 = -\dfrac{2}{ 3}$

Putting the values in the formula:

$tan \theta = |\dfrac{(\dfrac{3}{4}- (-\dfrac{2}{3}))}{ (1 + \dfrac{3}{4}\times (-\dfrac{2}{3 }))}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{3}{4}+\dfrac{2}{3}}{ (1 -\dfrac{1}{2})}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{17}{12}}{ \dfrac{1}{2}}|\\\Rightarrow tan \theta = \dfrac{17}{6}\\\Rightarrow \theta = tan^{-1}(\frac{17}{6})\\\Rightarrow \theta = \bold{70.69^\circ}$

So, correct answer is A. 70.69