How do you calculate the angle of the sun at any lattitude on the solstices?

Question

Looking for the equation for the angle of the sun at any lattitude on the summer solstice and winter solstice.
How high is the sun at 51*N in summer and winter? Or 49*N? Or any other lattitude?
Looking for the math equation, not using direct measurement with a sextant.

Can this equation be expanded to any time of year? If so, how?

Answer 1

Here is an example for 50° N latitude.
The earth's axis is tilted 23.5°.

On the summer solstice the sun will reach an angle in the sky of:
(90 - 50) + 23.5 = 40 + 23.5 = 63.5°

On the winter solstice the sun will reach an angle in the sky of:
(90 - 50) - 23.5 = 40 - 23.5 = 16.5°

See the following link.

http://www.physicalgeography.net/fundamentals/6h.html

Answer 2

The noon sun is overhead (90°) on the 23.5° latitude (North for the summer solstice June 21, South for the winter solstice Dec 22). Above and below this latitude, the angle decreases proportionately.

So at the equator (0°N) and at 43°N on the summer solstice, the angle is 66.5°. At 66.5°N (Arctic Circle), it's 43° in the sky. At the North Pole, it's 23.5°.
For the southern hemisphere on the same June solstice, the angle is 43° on the 23.5° latitude, 0° on the Antarctic Circle and 23.5° BELOW the horizon at the South Pole.