By Daniel Correia, IFSULDEMINAS Brazil
According to some historians, Tales probably spent a period of his life in Egypt and Babylon, devoting himself to research in contact with astronomers and mathematicians. In the period in which it passed in Egypt, it was realized that the Egyptians could not calculate the height of a great pyramid of Cheops and presented a solution to the problem. Tales supposed that the rays of the Sun are parallel when they reach the Earth, because of the distance that separates it from the Sun. (A.J. Philippi .; M.A. Romero; G.C. Bruna (editors)). Let us consider that Tales has chosen a position of illumination of the Sun, such that it is possible to calculate the height of the pyramid given the value of A in meters (width of the pyramid), the value of B in meters (length of the leftover pyramid), of C in meters (the height of any rod) and the value of D in meters (rod length), as shown in the figure.
Suppose we go back in time and that Tales has now been hired by the Egyptians to calculate the height of all the pyramids in Egypt. However, he does not understand much of programming and asked for his help to develop a system that allows him, through his Tablet, to enter with the data that is provided and the system generate the height of the pyramid.
The input is composed of several test cases. Each test case has a single line containing a real value A (2 <= A <= 10000), a value B (2 <= B <= 20000), a value C (1 <= C <= 100) and a value D (1 <= D <= 200). The data entry is finalized when the values A = 0, B = 0, C = 0 and D = 0 are read.
For each test case in your program, you must print a single line containing a real number with five decimal digits.
|Input Sample||Output Sample|
4 3 2 3