# High Noon

Geometry Level 5

On a specific day, Earth's axis of rotation is along the unit vector which has spherical coordinates

$r = 1, \theta = 23.44^{\circ}, \phi = -45^{\circ}$

with respect to a frame centered at the center of Earth, and with its z-axis perpendicular to the orbital plane of Earth around the Sun, and with its x-axis passing through the center of the Sun.

With respect to a point on Earth that has a latitude of $$30^{\circ}$$ North, what is the maximum angle of elevation of the Sun above the horizon ? (In degrees, correct to two decimal places)

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