# Thread: How do I find this point?

1. ## How do I find this point?

Originally Posted by earboth
1. Calculate the length $\displaystyle |\overline{PQ}|\approx 831$

2. Calculate all interior angles of the triangle OPQ:
$\displaystyle \angle(POQ) = 6.9105^\circ$
$\displaystyle \angle(QPO) = 21.4895^\circ$
$\displaystyle \angle(PQO) = 151.6^\circ$

3. Use the Sine rule to calculate the length of x:

$\displaystyle \dfrac x{831}=\dfrac{\sin(21.4893)}{\sin(151.6)}~\implies ~x \approx 640$

4. The coordinates of Q are $\displaystyle Q\left(x \cdot \cos(36.87^\circ)\ ,\ x \cdot \sin(36.87^\circ) \right)$
O = (0,0)
Q = (512,384)
P = (600,575)

Instead of finding what point Q is, how would I find out what point P, pretending it was unknown, is? I am unsure how to change the formula, stated above, around to find P.

Thanks

2. Never mind, I figured it out.

$\displaystyle ~x \approx 210.297$

The coordinates of P are $\displaystyle P\left(x \cdot \cos(65.3^\circ) + 512\ ,\ x \cdot \sin(65.3^\circ) + 384\right)$