The mathematical figure with four corners is called a trapeze if couple of its opposite sides are parallel, and other couple does not. The parallel parties call the trapeze bases, two others - side. In a rectangular trapeze one of corners at side - a straight line.
Instruction
1. Task 1. Find the bases of BC and AD of a rectangular trapeze if AC diagonal length = is known to f; CD side length = c and a corner of ADC at it = α.Решение: Consider a rectangular triangle of CED. The hypotenuse of c and a corner between a hypotenuse and a leg of EDC are known. Find lengths of the parties of CE and ED: on CE corner formula = CD*sin(ADC); ED = CD*cos(ADC). So: CE = c*sinα; ED=c*cosα.
2. Consider a rectangular triangle of ACE. The hypotenuse of AC and a leg of CE are known to you, find the party of AE by the rule of a rectangular triangle: the sum of squares of legs is equal to a hypotenuse square. So: AE(2) = AC(2) - CE(2) = f(2) - c*sinα. Calculate a square root from the right part of equality. You found the top basis of a rectangular trapeze.
3. Length of the basis of AD is the sum of lengths of two pieces of AE and ED. AE = a square root (f(2) - c*sinα); ED = c*cosα). So: AD = a square root (f(2) - c*sinα) + found c*cosα.Вы the lower basis of a rectangular trapeze.
4. Task 2. Find the bases of BC and AD of a rectangular trapeze if BD diagonal length = is known to f; CD side length = c and a corner of ADC at it = α.Решение: Consider a rectangular triangle of CED. Find lengths of the parties of CE and ED: CE = CD*sin(ADC) = c*sinα; ED = CD*cos(ADC) = c*cosα.
5. Consider ABCE rectangle. On property of a rectangle of AB = CE = c*sinα.Рассмотрите a rectangular triangle of ABD. On property of a rectangular triangle the square of a hypotenuse is equal to the sum of squares of legs. Therefore AD(2) = BD(2) - AB(2) = f(2) - c*sinα.Вы found the lower basis of a rectangular trapeze of AD = a square root (f(2) - c*sinα).
6. By the rule of a rectangle of BC = AE = AD - ED = a square root (f(2) - c*sinα) - с*cosα.Вы found the top basis of a rectangular trapeze.