Calculating 3D position of target given azimuth and elevation from different positions Situation is the following:
I have 2 sensors in space, their positions are known $(S_1x,S_1y,S_1z) ; (S_2x,S_2y,S_2z)$. $y$ axis is forward-backwards, $x$ axis is left-right, $z$ axis is up-down.
Sensor 1 outputs the azimuth ($S_1\hat{}T$) ($+y$ axis would be 0 degrees, $+x$ axis would be +90 degrees, so on) from it's position to a target point whose position is unknown $(Tx,Ty,Tz)$, and it's 3D distance to said point $|\overline{S_1T}|$.
Sensor 2 outputs the elevation ($S_2\hat{}T$) ($+y$ axis would be 0 degrees, $+z$ axis would be +90 degrees, so on) from it's position to the same target point as Sensor 1, as well as it's own 3D distance to it $|\overline{S_2T}|$.
I want to compute the position of the target point from origin, but I'm not sure how to do it. Here is an example of how it should work (if it's possible to do it from this data).
$S_1 = (1,1,0.5)$ ; $S_1\hat{}T = 26.56°$ ; $|\overline{S_1T}| = 2.29$
$S_2 = (3,2,0)$ ; $S_2\hat{}T = 35.26°$ ; $|\overline{S_2T}| = 1.73$
$Result: T=(2,3,1)$
Thanks in advance.
 A: $p = S_1 + r_1 ( \cos(\theta_1) \sin(\phi_1) , \cos(\theta_1) \cos(\phi_1) , \sin(\theta_1) \hspace{50pt}(1) $
Also
$ p = S_2 + r_2 ( \cos(\theta_2) \sin(\phi_2) , \cos(\theta_2) \cos(\phi_2), \sin( \theta_2 )\hspace{50pt}(2) $
Writing down the above expressions components-wise
$S_{1x} +  r_1 \cos(\theta_1) \sin(\phi_1) = S_{2x} + r_2 \cos(\theta_2) \cos(\phi_2) \hspace{50pt}(3)$
$ S_{1y} + r_1 \cos(\theta_1) \cos(\phi_1) = S_{2y} + r_2 \cos(\theta_2) \cos(\phi_2) \hspace{50pt}(4)$
$S_{1z} + r_1 \sin(\theta_1) = S_{2z} + r_2 \sin(\theta_2)\hspace{50pt}(5) $
What is known is $ \phi_1 $ and $\theta_2 $ and what is unknown is $\theta_1$ and $\phi_2 $
From equation $(5)$, we can solve for $\theta_1$, then from equation $(3)$, we can solve for $\phi_2 $
For the given example, and using equation $(5)$
$ 0.5 + 2.29 \sin(\theta_1) = 0 + 1.73 \sin(35.26^\circ) $
From which $\theta_1 = 12.578^\circ $
Using this in equation $(3)$
$ 1 + 2.29 \cos(12.578) \sin(26.56^\circ) = 3 + 1.73 \cos(35.26^\circ) \sin(\phi_2)$
From which $ \phi_2 = -45^\circ  $
Now all the angles are known, so using equation $(1)$
$p = (1, 1, 0.5) +2.29 ( \cos(12.578^\circ) \sin(26.56^\circ) , \cos(12.578^\circ) \cos(26.56^\circ) , \sin(12.578) = (2, 3, 1) $
And using equation $(2)$ for verification
$ p = (3,2,0) + 1.73 ( \cos(35.26^\circ) \sin(-45^\circ) , \cos(35.26^\circ) \cos(-45^\circ) , \sin(35.26^\circ) ) = (2, 3, 1 ) $
