Triangle calculator

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

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 100   b = 120   c = 150

Area: T = 5981.168836412
Perimeter: p = 370
Semiperimeter: s = 185

Angle ∠ A = α = 41.65496722739° = 41°38'59″ = 0.72769239136 rad
Angle ∠ B = β = 52.89109950542° = 52°53'28″ = 0.92331220084 rad
Angle ∠ C = γ = 85.45993326719° = 85°27'34″ = 1.49215467317 rad

Height: ha = 119.6233367282
Height: hb = 99.68661394021
Height: hc = 79.74989115217

Median: ma = 126.2933309403
Median: mb = 112.4722218792
Median: mc = 81.08663737011

Inradius: r = 32.33106398061
Circumradius: R = 75.23661365882

Vertex coordinates: A[150; 0] B[0; 0] C[60.33333333333; 79.74989115217]
Centroid: CG[70.11111111111; 26.58329705072]
Coordinates of the circumscribed circle: U[75; 5.95661941466]
Coordinates of the inscribed circle: I[65; 32.33106398061]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.3550327726° = 138°21'1″ = 0.72769239136 rad
∠ B' = β' = 127.1099004946° = 127°6'32″ = 0.92331220084 rad
∠ C' = γ' = 94.54106673281° = 94°32'26″ = 1.49215467317 rad

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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 = 100 ; ; b = 120 ; ; c = 150 ; ;

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

p = a+b+c = 100+120+150 = 370 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 370 }{ 2 } = 185 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 185 * (185-100)(185-120)(185-150) } ; ; T = sqrt{ 35774375 } = 5981.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5981.17 }{ 100 } = 119.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5981.17 }{ 120 } = 99.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5981.17 }{ 150 } = 79.75 ; ;

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{ 100**2-120**2-150**2 }{ 2 * 120 * 150 } ) = 41° 38'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 120**2-100**2-150**2 }{ 2 * 100 * 150 } ) = 52° 53'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 150**2-100**2-120**2 }{ 2 * 120 * 100 } ) = 85° 27'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5981.17 }{ 185 } = 32.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 100 }{ 2 * sin 41° 38'59" } = 75.24 ; ;




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