Question

an acute angle between given pair of lines 12x-4y=5 and 4x+2y=7 is 1 ( whether the statement is true or false)​

Answer 1

The given statement is false.

Step-by-step explanation:

The given equations of lines are

$12x-4y=5$

$4x+2y=7$

If a line is defined as $ax+by=c$, then the slope of the line is

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

Slope of first line is

$m_1=-\frac{12}{-4}=3$

Slope of second line is

$m_2=-\frac{4}{2}=-2$

Angle between two lines is

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

$\tan \theta =|\dfrac{3-(-2)}{1+(3)(-2)}|$

$\tan \theta =|\dfrac{5}{-5}|$

$\tan \theta =1$

Taking tan inverse on both sides.

$\theta =\tan^{-1}(1)$

$\theta =\frac{\pi}{4}$

$\theta =45^{\circ}$

Therefore, the acute angle between given pair of lines is 45° and the given statement is false.

#Learn more

Find the acute angle between lines having slope 3 and -2.

https://brainly.in/question/14227412

Find the acute angle between the lines whose slopes are 2 and 1/3. ?

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Answer 2

Answer:

find the acute angle between following pair of liney=2x+3 and y=3x+7