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If the altitude of the North Star is 30º above the horizon, then what is the highest altitude that the Sun will reach during the Autumnal Equinox: degrees

Question

If the altitude of the North Star is 30º above the horizon, then what is the highest altitude that the Sun will reach during the Autumnal Equinox: degrees

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Solution

The altitude of the North Star above the horizon is equal to the observer's latitude. So, if the North Star is 30º above the horizon, the observer is at 30º latitude.

During the Autumnal Equinox, the Sun is directly above the equator. For an observer at the equator (0º latitude), the Sun would reach an altitude of 90º (directly overhead) at noon.

However, for an observer at 30º latitude, the highest altitude the Sun would reach would be 60º. This is because the Sun's altitude decreases by 1º for every degree of latitude away from the equator. So, at 30º latitude, the Sun's maximum altitude would be 90º - 30º = 60º.

So, the highest altitude that the Sun will reach during the Autumnal Equinox for an observer at 30º latitude is 60º.

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