Astronomy Navigational question

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Please show all work. For the following problem:

  • Latitude=90-solar altitude + Declination of the Sun
  • Longitude = (UTC clock noon time– 1200) x 15 degrees
  • Solar DEC: Mar 21= 0 degrees JUN 21= 23.5 degrees
  • Sep 21 = 0 degrees Dec 21 = – 23.5 degrees

A ships navigator takes Sun shots and determines that the altitude of the Sun at noon is 27.5 degrees. The date is September 21, the autumnal equinox, when the Sun’s declination is 0 degrees. What is the latitude of the ship?