Question

29 Question * (1 Point) The acute angle between the lines x-3y- 6 = 0 and y = 2x + 5 is: 135° b. 45° c. 90° a​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The acute angle between the lines x-3y- 6 = 0 and y = 2x + 5 is:

a. 135°

b. 45°

c. 90°

EVALUATION

Here we have to find the acute angle between the lines x-3y- 6 = 0 and y = 2x + 5

First line is x-3y- 6 = 0

Slope of the line is given by

$\displaystyle \sf{m_1 = \frac{1}{3} }$

Second line is y = 2x + 5

Slope of the line is given by

$\displaystyle \sf{m_2 = 2 }$

Let θ be the acute angle

Then

$\displaystyle \sf{ \tan \theta = \bigg| \frac{m_1 -m_2 }{1 + m_1m_2} \bigg|}$

$\displaystyle \sf{ \implies \: \tan \theta = \bigg| \frac{ \frac{1}{3} -2 }{1 + \frac{1}{3} \times 2 } \bigg|}$

$\displaystyle \sf{ \implies \: \tan \theta = \bigg| \frac{ - \frac{5}{3} }{1 + \frac{2}{3} } \bigg|}$

$\displaystyle \sf{ \implies \: \tan \theta = \bigg| \frac{ - \frac{5}{3} }{ \frac{5}{3} } \bigg|}$

$\displaystyle \sf{ \implies \: \tan \theta = 1}$

$\displaystyle \sf{ \implies \: \theta = {45}^{ \circ} }$

FINAL ANSWER

Hence the correct option is b. 45°

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