Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and angle γ.

Obtuse scalene triangle.

Sides: a = 0.03   b = 0.33   c = 0.34114264179

Area: T = 0.00546514785
Perimeter: p = 0.70114264179
Semiperimeter: s = 0.35107132089

Angle ∠ A = α = 4.73661699856° = 4°44'10″ = 0.08326617602 rad
Angle ∠ B = β = 65.26438300144° = 65°15'50″ = 1.13990687162 rad
Angle ∠ C = γ = 110° = 1.92198621772 rad

Height: ha = 0.31100985649
Height: hb = 0.02881907786
Height: hc = 0.02772473261

Median: ma = 0.33554265932
Median: mb = 0.17875133781
Median: mc = 0.1660489876

Inradius: r = 0.01332629121
Circumradius: R = 0.18216692024

Vertex coordinates: A[0.34114264179; 0] B[0; 0] C[0.01325532156; 0.02772473261]
Centroid: CG[0.11879932111; 0.0099082442]
Coordinates of the circumscribed circle: U[0.17107132089; -0.06221345267]
Coordinates of the inscribed circle: I[0.02107132089; 0.01332629121]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.2643830014° = 175°15'50″ = 0.08326617602 rad
∠ B' = β' = 114.7366169986° = 114°44'10″ = 1.13990687162 rad
∠ C' = γ' = 70° = 1.92198621772 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and angle γ.

a = 0.03 ; ; b = 0.33 ; ; gamma = 110° ; ;

2. Calculation of the third side c of the triangle using a Law of Cosines

c**2 = a**2+b**2 - 2ab cos gamma ; ; c = sqrt{ a**2+b**2 - 2ab cos gamma } ; ; c = sqrt{ 0.03**2+0.33**2 - 2 * 0.03 * 0.33 * cos 110° } ; ; c = 0.34 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 0.03 ; ; b = 0.33 ; ; c = 0.34 ; ;

3. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 0.03+0.33+0.34 = 0.7 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.7 }{ 2 } = 0.35 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.35 * (0.35-0.03)(0.35-0.33)(0.35-0.34) } ; ; T = sqrt{ 0 } = 0 ; ;

6. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0 }{ 0.03 } = 0.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0 }{ 0.33 } = 0.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0 }{ 0.34 } = 0.03 ; ;

7. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 0.33**2+0.34**2-0.03**2 }{ 2 * 0.33 * 0.34 } ) = 4° 44'10" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.03**2+0.34**2-0.33**2 }{ 2 * 0.03 * 0.34 } ) = 65° 15'50" ; ; gamma = 180° - alpha - beta = 180° - 4° 44'10" - 65° 15'50" = 110° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0 }{ 0.35 } = 0.01 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.03 }{ 2 * sin 4° 44'10" } = 0.18 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.33**2+2 * 0.34**2 - 0.03**2 } }{ 2 } = 0.335 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.34**2+2 * 0.03**2 - 0.33**2 } }{ 2 } = 0.178 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.33**2+2 * 0.03**2 - 0.34**2 } }{ 2 } = 0.16 ; ;
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