# Thread: Trig and geometry problems

1. ## Trig and geometry problems

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

2. ## Re: Trig and geometry problems

Assuming $\theta$ is the first-quadrant angle between the two lines, suppose that $\alpha$ is the first-quadrant angle between the x-axis and the line y = 0.5. Then,

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

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

Replace $\tan \alpha$ with 0.5, then solve for $\tan \theta$.

3. ## Re: Trig and geometry problems

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.
$\theta=\arctan(5)-\arctan(0.5)$

4. ## Re: Trig and geometry problems

Darn, should've thought of that. Good solution.