Triangle calculator SAS

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


Right scalene triangle.

Sides: a = 500   b = 1886   c = 1951.152247995

Area: T = 471500
Perimeter: p = 4337.152247995
Semiperimeter: s = 2168.576623997

Angle ∠ A = α = 14.84881879762° = 14°50'53″ = 0.25991497681 rad
Angle ∠ B = β = 75.15218120238° = 75°9'7″ = 1.31216465587 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 1886
Height: hb = 500
Height: hc = 483.3044103442

Median: ma = 1902.497730617
Median: mb = 1067.356607929
Median: mc = 975.5766239973

Inradius: r = 217.4243760027
Circumradius: R = 975.5766239973

Vertex coordinates: A[1951.152247995; 0] B[0; 0] C[128.1299401761; 483.3044103442]
Centroid: CG[693.0943960569; 161.1011367814]
Coordinates of the circumscribed circle: U[975.5766239973; -0]
Coordinates of the inscribed circle: I[282.5766239973; 217.4243760027]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.1521812024° = 165°9'7″ = 0.25991497681 rad
∠ B' = β' = 104.8488187976° = 104°50'53″ = 1.31216465587 rad
∠ C' = γ' = 90° = 1.57107963268 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 = 500 ; ; b = 1886 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 500**2+1886**2 - 2 * 500 * 1886 * cos(90° ) } ; ; c = 1951.15 ; ;


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 = 500 ; ; b = 1886 ; ; c = 1951.15 ; ;

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

p = a+b+c = 500+1886+1951.15 = 4337.15 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4337.15 }{ 2 } = 2168.58 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2168.58 * (2168.58-500)(2168.58-1886)(2168.58-1951.15) } ; ; T = sqrt{ 222312250000 } = 471500 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 471500 }{ 500 } = 1886 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 471500 }{ 1886 } = 500 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 471500 }{ 1951.15 } = 483.3 ; ;

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{ 500**2-1886**2-1951.15**2 }{ 2 * 1886 * 1951.15 } ) = 14° 50'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1886**2-500**2-1951.15**2 }{ 2 * 500 * 1951.15 } ) = 75° 9'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1951.15**2-500**2-1886**2 }{ 2 * 1886 * 500 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 471500 }{ 2168.58 } = 217.42 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 500 }{ 2 * sin 14° 50'53" } = 975.58 ; ;




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