# Trig and geometry problems

• Jun 30th 2012, 08:12 AM
Pat722
Trig and geometry problems
given y = 5x and y = .5x, When the these lines cross, what is the value of tan theta?
• Jun 30th 2012, 08:38 AM
richard1234
Re: Trig and geometry problems
Assuming $\displaystyle \theta$ is the first-quadrant angle between the two lines, suppose that $\displaystyle \alpha$ is the first-quadrant angle between the x-axis and the line y = 0.5. Then,

$\displaystyle \tan \alpha = 0.5$, and
$\displaystyle \tan (\alpha + \theta) = 5$.

Also, $\displaystyle \tan (\alpha + \theta) = \frac{\tan \alpha + \tan \theta}{1 - \tan \alpha \tan \theta} = 5$.

Replace $\displaystyle \tan \alpha$ with 0.5, then solve for $\displaystyle \tan \theta$.
• Jun 30th 2012, 09:59 AM
Plato
Re: Trig and geometry problems
Quote:

Originally Posted by Pat722
given y = 5x and y = .5x, When the these lines cross, what is the value of tan theta?

Here is a simple way.
$\displaystyle \theta=\arctan(5)-\arctan(0.5)$
• Jun 30th 2012, 10:04 AM
richard1234
Re: Trig and geometry problems
Darn, should've thought of that. (Headbang) Good solution.