The zenith distance is the complement of which angle?

• A. Altitude
• B. Azimuth
• C. Declination
• D. Polar Distance

Answer: (A)

The zenith distance is the angular distance from the object to the zenith, the point directly overhead. The altitude is the angle of the object above the horizon. On the celestial dome, the horizon and the zenith form a right angle, so the angle from the horizon up to the object (the altitude) and the angle from the object up to the zenith (the zenith distance) add to 90 degrees. In equation form, z = 90° − h, so the zenith distance is the complement of altitude.

Other measures describe different things: azimuth is the horizontal direction around the horizon, declination is the object's position north or south of the celestial equator, and polar distance is the angular distance to the celestial pole. None of these are the complementary relation to zenith distance.