Instructor key. Numeric values are generated by build_astr476_package.py from the computation module and the included source subset.
Solution 1
theta=0.596506 deg = 35.7904 arcmin = 0.01041100 rad; sigma_theta=0.00000300 rad = 0.00017189 deg = 0.010313 arcmin.
Solution 2
The sound horizon is set by pre-recombination baryon-photon physics; D_M(z*) integrates the expansion and depends on late geometry as well as curvature/model assumptions.
Solution 3
The curve is a theoretical illustrative acoustic oscillation, not fetched Planck bandpowers; caption it as a schematic with no observational points or likelihood.
Solution 4
H0 inference requires a calibrated r_s and assumptions about early expansion, curvature, and late-time model; the angle alone is a ratio.