Triangle calculator

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

You have entered side b, c and angle γ.

Triangle has two solutions: a=3.894395228; b=45; c=42 and a=67.02770155446; b=45; c=42.

#1 Obtuse scalene triangle.

Sides: a = 3.894395228   b = 45   c = 42

Area: T = 53.94105191246
Perimeter: p = 90.894395228
Semiperimeter: s = 45.447697614

Angle ∠ A = α = 3.27222167114° = 3°16'20″ = 0.05771109555 rad
Angle ∠ B = β = 138.7287783289° = 138°43'40″ = 2.42112565824 rad
Angle ∠ C = γ = 38° = 0.66332251158 rad

Height: ha = 27.70547663897
Height: hb = 2.39773564055
Height: hc = 2.56985961488

Median: ma = 43.48222870133
Median: mb = 19.57988516563
Median: mc = 24.06441108745

Inradius: r = 1.18768890673
Circumradius: R = 34.11096541551

Vertex coordinates: A[42; 0] B[0; 0] C[-2.92766325672; 2.56985961488]
Centroid: CG[13.02444558109; 0.85661987163]
Coordinates of the circumscribed circle: U[21; 26.87987742761]
Coordinates of the inscribed circle: I[0.447697614; 1.18768890673]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.7287783289° = 176°43'40″ = 0.05771109555 rad
∠ B' = β' = 41.27222167114° = 41°16'20″ = 2.42112565824 rad
∠ C' = γ' = 142° = 0.66332251158 rad




How did we calculate this triangle?

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 = 3.89 ; ; b = 45 ; ; c = 42 ; ;

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

p = a+b+c = 3.89+45+42 = 90.89 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 90.89 }{ 2 } = 45.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 45.45 * (45.45-3.89)(45.45-45)(45.45-42) } ; ; T = sqrt{ 2909.58 } = 53.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 53.94 }{ 3.89 } = 27.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 53.94 }{ 45 } = 2.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 53.94 }{ 42 } = 2.57 ; ;

5. 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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 3.89**2-45**2-42**2 }{ 2 * 45 * 42 } ) = 3° 16'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 45**2-3.89**2-42**2 }{ 2 * 3.89 * 42 } ) = 138° 43'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 42**2-3.89**2-45**2 }{ 2 * 45 * 3.89 } ) = 38° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 53.94 }{ 45.45 } = 1.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.89 }{ 2 * sin 3° 16'20" } = 34.11 ; ;





#2 Obtuse scalene triangle.

Sides: a = 67.02770155446   b = 45   c = 42

Area: T = 928.484390373
Perimeter: p = 154.0277015545
Semiperimeter: s = 77.01435077723

Angle ∠ A = α = 100.7287783289° = 100°43'40″ = 1.75880314666 rad
Angle ∠ B = β = 41.27222167114° = 41°16'20″ = 0.72203360712 rad
Angle ∠ C = γ = 38° = 0.66332251158 rad

Height: ha = 27.70547663897
Height: hb = 41.26659512769
Height: hc = 44.21435192252

Median: ma = 27.77330948365
Median: mb = 51.20660582979
Median: mc = 53.08330519696

Inradius: r = 12.05661175641
Circumradius: R = 34.11096541551

Vertex coordinates: A[42; 0] B[0; 0] C[50.37664382479; 44.21435192252]
Centroid: CG[30.79221460826; 14.73878397417]
Coordinates of the circumscribed circle: U[21; 26.87987742761]
Coordinates of the inscribed circle: I[32.01435077723; 12.05661175641]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 79.27222167114° = 79°16'20″ = 1.75880314666 rad
∠ B' = β' = 138.7287783289° = 138°43'40″ = 0.72203360712 rad
∠ C' = γ' = 142° = 0.66332251158 rad

Calculate another triangle

How did we calculate this triangle?

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 = 67.03 ; ; b = 45 ; ; c = 42 ; ;

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

p = a+b+c = 67.03+45+42 = 154.03 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 154.03 }{ 2 } = 77.01 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 77.01 * (77.01-67.03)(77.01-45)(77.01-42) } ; ; T = sqrt{ 862082.36 } = 928.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 928.48 }{ 67.03 } = 27.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 928.48 }{ 45 } = 41.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 928.48 }{ 42 } = 44.21 ; ;

5. 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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 67.03**2-45**2-42**2 }{ 2 * 45 * 42 } ) = 100° 43'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 45**2-67.03**2-42**2 }{ 2 * 67.03 * 42 } ) = 41° 16'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 42**2-67.03**2-45**2 }{ 2 * 45 * 67.03 } ) = 38° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 928.48 }{ 77.01 } = 12.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 67.03 }{ 2 * sin 100° 43'40" } = 34.11 ; ;




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