Scientists can estimate the depth of craters on the moon by studying the lengths of their shadows in the craters. find the depth of a crater, if the shadow is estimated to be 400 m long and the angle of elevation of the sun is 48°.

It's a much more interesting problem when we have to estimate the shadow length from a photo.

The crater is a curvy bumpy surface, but let's approximate it as part of a sphere and just conflate the arc and chord length, so the 400 m shadow corresponds to a 400 m chord from the edge at the surface to the bottom.

The shadow as a chord forms a hypotenuse right triangle with the depth d being the leg opposite the 48 degree angle of the sun.

297 m

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step-by-step explanation: