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Angelina_Jolie [31]
4 years ago
5

Calculate, correct to one decimal plice

Mathematics
1 answer:
inn [45]4 years ago
4 0

Answer:

<em>A. 70.69 </em>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 <em>A. 70.69</em>

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