Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 68   b = 110   c = 75.46

Area: T = 2526.675478926
Perimeter: p = 253.46
Semiperimeter: s = 126.73

Angle ∠ A = α = 37.50223009896° = 37°30'8″ = 0.65545386293 rad
Angle ∠ B = β = 99.99883761296° = 99°59'54″ = 1.74553009101 rad
Angle ∠ C = γ = 42.49993228809° = 42°29'58″ = 0.74217531141 rad

Height: ha = 74.31439643901
Height: hb = 45.9439541623
Height: hc = 66.96772618411

Median: ma = 87.98435541451
Median: mb = 46.19663829753
Median: mc = 83.29773414942

Inradius: r = 19.93774638149
Circumradius: R = 55.84881845782

Vertex coordinates: A[75.46; 0] B[0; 0] C[-11.80661781076; 66.96772618411]
Centroid: CG[21.21879406308; 22.32224206137]
Coordinates of the circumscribed circle: U[37.73; 41.1766046686]
Coordinates of the inscribed circle: I[16.73; 19.93774638149]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.498769901° = 142°29'52″ = 0.65545386293 rad
∠ B' = β' = 80.00216238704° = 80°6″ = 1.74553009101 rad
∠ C' = γ' = 137.5010677119° = 137°30'2″ = 0.74217531141 rad

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How did we calculate this triangle?

a = 68 ; ; b = 110 ; ; c = 75.46 ; ;

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

p = a+b+c = 68+110+75.46 = 253.46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 253.46 }{ 2 } = 126.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 126.73 * (126.73-68)(126.73-110)(126.73-75.46) } ; ; T = sqrt{ 6384085.49 } = 2526.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2526.67 }{ 68 } = 74.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2526.67 }{ 110 } = 45.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2526.67 }{ 75.46 } = 66.97 ; ;

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{ 68**2-110**2-75.46**2 }{ 2 * 110 * 75.46 } ) = 37° 30'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 110**2-68**2-75.46**2 }{ 2 * 68 * 75.46 } ) = 99° 59'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 75.46**2-68**2-110**2 }{ 2 * 110 * 68 } ) = 42° 29'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2526.67 }{ 126.73 } = 19.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 68 }{ 2 * sin 37° 30'8" } = 55.85 ; ;




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