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Piece of Cake

By shajia, jackal_1586 · Limits 1s, 512 MB

Diya has got a nice birthday cake for Arshiya and Alayna, her twin daughters. The two sisters were amazed to see the strange triangular-shaped birthday cake. On the cake ABC, there is a line from one of the vertex A to the midpoint of the opposite line BC. On her daughter’s birthday, Diya declared a quiz competition. She told her daughters that she will make two more square-shaped cake as the prize of that quiz competition. Each side length of Arshiya’s cake will be equal to AB, one side of the triangle-shaped cake. Each side length of Alayna’s cake will be equal to AC, one side of the triangle-shaped cake. For getting the prize, Arshiya and Alayna have to calculate the sum of the area of these two square-shaped cake. As they want to win the prize, they want your help.  You will be given some information about the triangle-shaped cake for solving the challenge. You will be given AB, the one side of the triangular-shaped cake, AD, the line from vertex A to the midpoint of BC and the angle DAB.

Consider $\pi = cos^{-1}(-1.0) $ if needed.

Input

First line of the input contains an integer T(1 < T < 100000) which denotes the number of test cases. Then for each test case, there will be three real number X which denotes the length of AB, Y which denotes the length of AD and A which denotes the angle DAB. All lengths are less than 104, also angles and lengths are greater than zero.

It is guaranteed that the input forms a valid triangle with positive area.

Output

For each test case, output the total sum of the area of the two square-shaped cake. Absolute error less than 10-6 will be ignored.

Sample

InputOutput
2
100 86.60254037844386 30
30.341180 50.312433 52.911429
20000.000000000
8284.228534779


Discussion
Statistics

90% Solution Ratio

JU_FIREW0RKSEarliest, 1w ago

CUET_DEADBITFastest, 0.1s

Noshin_1703086Lightest, 1.3 MB

RafeedShortest, 142B

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