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Very Easy Geometry

Limits 1s, 512 MB

In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

You are given an isosceles triangle of OCD where OD = OC and OA = OB. As you are good in mathematics you have to calculate the area of ABCD where you will be given the angle of ∠COD and the value of OD and OA respectively.

Input

The Input starts with an integer T (T ≤ 1000), denoting the number of test cases.

Each case contains three floating point numbers the value of ∠COD (in radian, 0 ≤ ∠COD ≤ 1000), OA (0 ≤ OD ≤ 1000) and OC (0 ≤ OB ≤ 100000).

Output

For each case, print the case number and the area of ABCD rounded to eight places after the decimal point.

Sample

InputOutput
4
0.2 2 5
1 2 3
3 10 170
0.000000000000001111111 0.02222258 11111.111111111115
Case 1: 2.08336663
Case 2: 1.78661943
Case 3: 1889.18411647
Case 4: 0.00000007

The area of an isosceles triangle is 12×ab×sin(θ) \frac{1}{2} \times ab \times sin(θ)

Discussion

Statistics


92% Solution Ratio

NAbdullaEarliest, Apr '19

NAbdullaFastest, 0.0s

N550999.Lightest, 0 B

mdvirusShortest, 137B

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Editorial

This is a very easy Geometry problem. You have to calculate the area of the triangle first then calc...

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