# Math Help - Solve for Theta

1. ## Solve for Theta

I need to solve for theta with only the info shown in the image below.

Thanks.

2. is 36.00 lint is deflected $\theta$ from the vertical line?

3. ## Yes

yes the angle between the vetical line on the left and the 36.00 line is .

4. $sin \theta = \frac{36cos\theta -12}{128}$

$36cos\theta - 128sin\theta = 12$
$
9cos\theta - 32sin\theta = 3$

$\frac{9}{\sqrt{9^2+32^2}}cos\theta - \frac{32}{\sqrt{9^2+32^2}}sin\theta = \frac{3}{\sqrt{9^2+32^2}}$

$sin\alpha cos\theta - cos\alpha sin\theta = \frac{3}{\sqrt{9^2+32^2}}$

$sin(\alpha - \theta) = \frac{3}{\sqrt{9^2+32^2}}$

$\theta = \alpha - sin^-1(\frac{3}{\sqrt{9^2+32^2}})$

where $\alpha = sin^-1(\frac{9}{\sqrt{9^2+32^2}})$