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1

Part of 1963 Czech and Slovak Olympiad III A

Problems(1)

Sides of a cuboid

Source: Czech and Slovak Olympiad 1963, National Round, Problem 1

6/16/2024
Consider a cuboidABCDA′B′C′D′ ABCDA'B'C'D' (where ABCDABCD is a rectangle and AA′∥BB′∥CC′∥DD′AA' \parallel BB' \parallel CC' \parallel DD') with AA′=dAA' = d, ∠ABD′=α,∠A′D′B=β\angle ABD' = \alpha, \angle A'D'B = \beta. Express the lengths x = ABAB, y=BCy = BC in terms of dd and (acute) angles α,β\alpha, \beta. Discuss condition of solvability.
geometryrectangle3D geometrycomputation