file.jpg I need to find a...

2. ## I need your help with this Trigo Challenge...

file.jpgUnknown: a and b.
Known: all the angles and d.

My work so far:

math.jpg

3. file.jpg

I can't speak for others, but I'm having trouble deciphering even the correctly-oriented image. And I think I'm seeing query-marks by many of the items, such as along the red line paralleling the right-hand triangle's hypotenuse.

Please reply with clarifications, including typing out relevant information, such as lines which are congruent (that is, which have the same length), and measures of any known angles. Thank you!

4. I posted the previous reply before I realized that you'd posted this twice. Sorry.

Originally Posted by cham07
file.jpgUnknown: a and b.
Known: all the angles and d.

My work so far:
Really? The image below looks to be the work of whoever sent this to you, who addressed you as "Jon".

Originally Posted by cham07
This image is also small, but I'm pretty sure the other helper said the following:

We have $a\, =\, \dfrac{P\, \cos(\theta)}{3}$ with $O\, =\, 2\, (a\, +\, d)\, \cos(\theta).$

The partial derivation $\dfrac{\partial}{\partial\, a}\, \left(2\, (a\, +\, d)\, \cos(\theta)\right)\, =\, 2\, \cos(\theta)$

Hence $a$ is equivalent to $a\, =\, \dfrac{O}{2\, \cos(\theta)}\, -\, d$

So we have the following equality:

. . . . .$\dfrac{1}{3}\, \left(O\, \cos(\theta)\right)\, =\, \dfrac{O}{2\, \cos(\theta)}\, -\, d$

Assuming that $d,\, O,$ and $\theta$ are positive

. . . . .$O\, \left(\cos(\theta)\right)\, =\, -6d\, \cos(\theta)$

Thus

. . . . .$O\, =\, -\dfrac{6d\, \cos(\theta)}{\cos(2\theta)\, -\, 2}$

Have you taken calculus and differential equations?