Right triangle calculator (a,b,c)

Please enter two properties of the right triangle

Use symbols: a, b, c, A, B, h, T, p, r, R


You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 1664.33   b = 1140   c = 2100

Area: T = 944843.3277489
Perimeter: p = 4904.33
Semiperimeter: s = 2452.165

Angle ∠ A = α = 52.12441371639° = 52°7'27″ = 0.91097378133 rad
Angle ∠ B = β = 32.72991574635° = 32°43'45″ = 0.57112315591 rad
Angle ∠ C = γ = 95.14767053725° = 95°8'48″ = 1.66106232812 rad

Height: ha = 1135.404382916
Height: hb = 1657.621987279
Height: hc = 899.8510788085

Median: ma = 1470.477659375
Median: mb = 1806.958798912
Median: mc = 965.5555370991

Inradius: r = 385.3109849659
Circumradius: R = 1054.255045192

Vertex coordinates: A[2100; 0] B[0; 0] C[1400.09438926; 899.8510788085]
Centroid: CG[1166.69879642; 299.9550262695]
Coordinates of the circumscribed circle: U[1050; -94.5732804627]
Coordinates of the inscribed circle: I[1312.165; 385.3109849659]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.8765862836° = 127°52'33″ = 0.91097378133 rad
∠ B' = β' = 147.2710842536° = 147°16'15″ = 0.57112315591 rad
∠ C' = γ' = 84.85332946275° = 84°51'12″ = 1.66106232812 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c

a = 1664.33 ; ; b = 1140 ; ; c = 2100 ; ;


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 = 1664.33 ; ; b = 1140 ; ; c = 2100 ; ; : Nr. 1

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

p = a+b+c = 1664.33+1140+2100 = 4904.33 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4904.33 }{ 2 } = 2452.17 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2452.17 * (2452.17-1664.33)(2452.17-1140)(2452.17-2100) } ; ; T = sqrt{ 892728913501 } = 944843.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 944843.33 }{ 1664.33 } = 1135.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 944843.33 }{ 1140 } = 1657.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 944843.33 }{ 2100 } = 899.85 ; ;

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{ 1664.33**2-1140**2-2100**2 }{ 2 * 1140 * 2100 } ) = 52° 7'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1140**2-1664.33**2-2100**2 }{ 2 * 1664.33 * 2100 } ) = 32° 43'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2100**2-1664.33**2-1140**2 }{ 2 * 1140 * 1664.33 } ) = 95° 8'48" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 944843.33 }{ 2452.17 } = 385.31 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1664.33 }{ 2 * sin 52° 7'27" } = 1054.25 ; ;
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