Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side b, c and angle α.

Obtuse scalene triangle.

Sides: a = 55.90215617376   b = 111   c = 125

Area: T = 3102.214387426
Perimeter: p = 291.9021561738
Semiperimeter: s = 145.9510780869

Angle ∠ A = α = 26.562° = 26°33'43″ = 0.46435943559 rad
Angle ∠ B = β = 62.61114841982° = 62°36'41″ = 1.09327765488 rad
Angle ∠ C = γ = 90.82765158018° = 90°49'35″ = 1.58552217489 rad

Height: ha = 110.988845105
Height: hb = 55.89657454822
Height: hc = 49.63554219882

Median: ma = 114.8555360558
Median: mb = 79.33994120369
Median: mc = 61.78797887853

Inradius: r = 21.2555205733
Circumradius: R = 62.50765034639

Vertex coordinates: A[125; 0] B[0; 0] C[25.71659384188; 49.63554219882]
Centroid: CG[50.23986461396; 16.54551406627]
Coordinates of the circumscribed circle: U[62.5; -0.90216514221]
Coordinates of the inscribed circle: I[34.95107808688; 21.2555205733]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.438° = 153°26'17″ = 0.46435943559 rad
∠ B' = β' = 117.3898515802° = 117°23'19″ = 1.09327765488 rad
∠ C' = γ' = 89.17334841982° = 89°10'25″ = 1.58552217489 rad

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How did we calculate this triangle?

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 = 55.9 ; ; b = 111 ; ; c = 125 ; ;

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

p = a+b+c = 55.9+111+125 = 291.9 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 291.9 }{ 2 } = 145.95 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 145.95 * (145.95-55.9)(145.95-111)(145.95-125) } ; ; T = sqrt{ 9623730.92 } = 3102.21 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3102.21 }{ 55.9 } = 110.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3102.21 }{ 111 } = 55.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3102.21 }{ 125 } = 49.64 ; ;

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{ 55.9**2-111**2-125**2 }{ 2 * 111 * 125 } ) = 26° 33'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 111**2-55.9**2-125**2 }{ 2 * 55.9 * 125 } ) = 62° 36'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 125**2-55.9**2-111**2 }{ 2 * 111 * 55.9 } ) = 90° 49'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3102.21 }{ 145.95 } = 21.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 55.9 }{ 2 * sin 26° 33'43" } = 62.51 ; ;




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