Triangle calculator SAS

Please enter two sides of the triangle and the included angle
°


Obtuse scalene triangle.

Sides: a = 65   b = 80   c = 128.8032930627

Area: T = 2129.795531515
Perimeter: p = 273.8032930627
Semiperimeter: s = 136.9011465313

Angle ∠ A = α = 24.41774986753° = 24°25'3″ = 0.4266165747 rad
Angle ∠ B = β = 30.58325013247° = 30°34'57″ = 0.53437653416 rad
Angle ∠ C = γ = 125° = 2.1821661565 rad

Height: ha = 65.53221635431
Height: hb = 53.24548828788
Height: hc = 33.07106033595

Median: ma = 102.1710678127
Median: mb = 93.8498801106
Median: mc = 34.13113824139

Inradius: r = 15.55771403876
Circumradius: R = 78.62196723336

Vertex coordinates: A[128.8032930627; 0] B[0; 0] C[55.95883344412; 33.07106033595]
Centroid: CG[61.5877088356; 11.02435344532]
Coordinates of the circumscribed circle: U[64.40114653134; -45.09443914842]
Coordinates of the inscribed circle: I[56.90114653134; 15.55771403876]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.5832501325° = 155°34'57″ = 0.4266165747 rad
∠ B' = β' = 149.4177498675° = 149°25'3″ = 0.53437653416 rad
∠ C' = γ' = 55° = 2.1821661565 rad

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How did we calculate this triangle?

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

a = 65 ; ; b = 80 ; ; gamma = 125° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 65**2+80**2 - 2 * 65 * 80 * cos(125° ) } ; ; c = 128.8 ; ;


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 = 65 ; ; b = 80 ; ; c = 128.8 ; ;

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

p = a+b+c = 65+80+128.8 = 273.8 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 273.8 }{ 2 } = 136.9 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 136.9 * (136.9-65)(136.9-80)(136.9-128.8) } ; ; T = sqrt{ 4536028.08 } = 2129.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2129.8 }{ 65 } = 65.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2129.8 }{ 80 } = 53.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2129.8 }{ 128.8 } = 33.07 ; ;

6. 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{ 65**2-80**2-128.8**2 }{ 2 * 80 * 128.8 } ) = 24° 25'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 80**2-65**2-128.8**2 }{ 2 * 65 * 128.8 } ) = 30° 34'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 128.8**2-65**2-80**2 }{ 2 * 80 * 65 } ) = 125° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2129.8 }{ 136.9 } = 15.56 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 65 }{ 2 * sin 24° 25'3" } = 78.62 ; ;




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