A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples. By John Casey.

Astronomy. 155
20. Determine the latitude, and the sun's declination, being given that
the sun sets at 3 o'clock, and is 18~ below the horizon at 4 o'clock.
21. Determine the latitudes of two places A, B from the following data:When the sun is in the tropic of Cancer, he rises an hour earlier at A
than at B; and when at the tropic of Capricorn, an hour earlier at B
than at A.
22. If in latitudes 11, 12,3 on the same day, on the same meridian, the
lengths of meridian shadows of towers of equal heights be s, sa, s3, prove
S1 (S2 - 83)2 S2 (83 - S1)2 83 (S1 - S2)2
tan (12 - k) tan(l3 - I) tan (hl - 12)
23. If the time of the sun, being due east, be midway between sunrise
and 12 o'clock, find the latitude, the declination being given.
24. If the sun be due east at a given place two hours after the rising,
find the declination.
25. Given the right ascension and declination of four stars, find the right
ascension and declination of the point in the heavens where the diagonals of
the spherical quadrilateral which they determine intersect each other.