Answer to Question #138286 in Physics for Ty

Question

Compare the annual variation in noon sun angle at 55° N to that at 15°N.

Answer 1

In the northern hemisphere, on the 22nd of June, the sun rays are perpendicular to the surface of Earth at 23.5°N.

Noon sun angle at 55° N:

$$\theta_{1s}=90-|55-23.5|=58.5°,\\ \theta_{2s}=90-|15-23.5|=81.5°.$$

Now consider the winter time, December 22, the sun rays are perpendicular to the earth surface at 23.5°S, or "-23.5°N":

$$\theta_{1w}=90-|55-(-23.5)|=11.5°,\\ \theta_{2w}=90-|15-(-23.5)|=51.5°.$$

The annual variations are

$$\Delta\theta_1=\theta_{1s}-\theta_{1w}=47°,\\ \Delta\theta_2=\theta_{2s}-\theta_{2w}=30°.$$