# Sphere + triangle - problems

- MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - Rotation of the Earth

Calculate the circumferential speed of the Earth's surface at a latitude of 61°. Consider a globe with a radius of 6378 km. - Elevation

What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km. - Horizon

The top of a lighthouse is 17 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.] - Moon

We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth. - Airplane

Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies? - Sphere from tree points

Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a

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See also our trigonometric triangle calculator.