Estimate the Angle
Turn the mirrors, switch on the light, find the sensor. Steer the beam over and under walls with the angles of incidence and reflection.
The Observatory
You are an observer in 1420s Samarkand. Line up the quadrant, measure on the great arc and fill the zij, line by line.
Goal: Measures altitude from the horizon; uses complementary angles, the fact that a star is highest as it crosses due south, and the proportion between arc length and angle.