Triangle calculator SAS

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


Acute isosceles triangle.

Sides: a = 58   b = 58   c = 52.66328979698

Area: T = 1360.767658454
Perimeter: p = 168.663289797
Semiperimeter: s = 84.33114489849

Angle ∠ A = α = 63° = 1.10995574288 rad
Angle ∠ B = β = 63° = 1.10995574288 rad
Angle ∠ C = γ = 54° = 0.94224777961 rad

Height: ha = 46.92329856737
Height: hb = 46.92329856737
Height: hc = 51.67883784029

Median: ma = 47.19884153472
Median: mb = 47.19884153472
Median: mc = 51.67883784029

Inradius: r = 16.13659326908
Circumradius: R = 32.54774608914

Vertex coordinates: A[52.66328979698; 0] B[0; 0] C[26.33114489849; 51.67883784029]
Centroid: CG[26.33114489849; 17.22661261343]
Coordinates of the circumscribed circle: U[26.33114489849; 19.13109175115]
Coordinates of the inscribed circle: I[26.33114489849; 16.13659326908]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117° = 1.10995574288 rad
∠ B' = β' = 117° = 1.10995574288 rad
∠ C' = γ' = 126° = 0.94224777961 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 = 58 ; ; b = 58 ; ; gamma = 54° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 58**2+58**2 - 2 * 58 * 58 * cos(54° ) } ; ; c = 52.66 ; ;


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 = 58 ; ; b = 58 ; ; c = 52.66 ; ;

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

p = a+b+c = 58+58+52.66 = 168.66 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 168.66 }{ 2 } = 84.33 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 84.33 * (84.33-58)(84.33-58)(84.33-52.66) } ; ; T = sqrt{ 1851685.7 } = 1360.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1360.77 }{ 58 } = 46.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1360.77 }{ 58 } = 46.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1360.77 }{ 52.66 } = 51.68 ; ;

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{ 58**2-58**2-52.66**2 }{ 2 * 58 * 52.66 } ) = 63° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 58**2-58**2-52.66**2 }{ 2 * 58 * 52.66 } ) = 63° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 52.66**2-58**2-58**2 }{ 2 * 58 * 58 } ) = 54° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1360.77 }{ 84.33 } = 16.14 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 58 }{ 2 * sin 63° } = 32.55 ; ;




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