The non-setting star has a height of 20 ° at the lower climax and 50 ° at the top. Find the declination of this star

The non-setting star has a height of 20 ° at the lower climax and 50 ° at the top. Find the declination of this star and the latitude of the observation site.

The problem has two solutions:
1) The star passes through the upper climax south of the zenith; then we have two equations: b = φ -40 ° and b = 110 ° – φ, whence we obtain b = 35 °, φ = 75 °.
2) The star passes through the upper culmination north of the zenith; then we have two equations: b = 40 ° + φ and b = 110 ° – φ, whence we obtain b = 75 °, φ = 35 °.

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