# Thread: angles between two lines

1. ## angles between two lines

Happy New Year!

There is a question on my exercise book that:

The slopes of lines L1 and L2 are the roots of the equation 6 x^2 - 5x - 1 = 0

If a is the acute angle between L1 and L2, find the value of tan a .

The answer I 've calculated is 7 / 5.
But the book says that it should be 1/7.
How can I get this or it's the mistake of the book?

2. Originally Posted by ling_c_0202
Happy New Year!

There is a question on my exercise book that:

The slopes of lines L1 and L2 are the roots of the equation 6 x^2 - 5x - 1 = 0

If a is the acute angle between L1 and L2, find the value of tan a .

The answer I 've calculated is 7 / 5.
But the book says that it should be 1/7.
How can I get this or it's the mistake of the book?
The solutions to,
$6x^2-5x-1$
Are,
$x=\frac{5\pm \sqrt{25+24}}{12}$

$x=\frac{5\pm 7}{12}$
Thus,
$x=1,-1/6$

The angle between two (non-perpendicular) lines is,
$\tan \theta = \frac{1+1/6}{1+(1)(-1/6)}$
Thus,
$\tan \theta = (7/6)(5/6)=1$
Thus,
$\tan \theta = 7/5$

3. Exactly the same as what I 've done. Thanks!