 Solution

The central value is $S=150\cos 45^{\circ }=106.07$. Treating the stated errors as independent standard uncertainties, convert the angular uncertainty to radians and propagate derivatives:The two measured values differ by $10.8/\sqrt{6.0^2+5.6^2}=1.32$ combined standard deviations. Our prediction differs from them by $0.19$ and $1.07$ combined standard deviations respectively. All three values are statistically compatible. If the input errors are strict bounds instead, the first-order bound on the calculated value is about $\pm 9.0$; consistency remains possible, but a Gaussian significance test then has no stated justification.