Problem 1650. LASER Tracker - Mirror Distance and Angle

Determine the mirror's distance and relative angle to the LASER Tracker given the distances to a reference SMR (Spherical Mounted Retro-reflector) and the angle to the SMR.

Theta is the included angle between d1 and d2.

Phi is the angle of interest and is between d2 and d3.

The Test method is locate the SMR to capture the mirror reflectance. Record L. Rotate the SMR to be directly viewed by the Tracker. Record d1 and Theta.

Given Theta, d1, and d2+d3 determine d2 and Phi.

Input: [d1, L, Theta] where L=d2+d3 and d1*cos(Theta) < d2

Output: [d2 Phi]

Examples:

Input: [2^.5, 2+2^.5, pi/4]..... Output: [2 pi/4]

Input: [2.3994, 4, .2991]..... Output: [3, pi/4 ]