Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 2.4   b = 4.7   c = 5.5

Area: T = 5.60879942939
Perimeter: p = 12.6
Semiperimeter: s = 6.3

Angle ∠ A = α = 25.71545167952° = 25°42'52″ = 0.44988029836 rad
Angle ∠ B = β = 58.17986314749° = 58°10'43″ = 1.01554086735 rad
Angle ∠ C = γ = 96.10768517299° = 96°6'25″ = 1.67773809964 rad

Height: ha = 4.67333285782
Height: hb = 2.38663805506
Height: hc = 2.03992706523

Median: ma = 4.97329267037
Median: mb = 3.53330581654
Median: mc = 2.52223996511

Inradius: r = 0.89901578244
Circumradius: R = 2.76656946829

Vertex coordinates: A[5.5; 0] B[0; 0] C[1.26554545455; 2.03992706523]
Centroid: CG[2.25551515152; 0.68797568841]
Coordinates of the circumscribed circle: U[2.75; -0.29442228386]
Coordinates of the inscribed circle: I[1.6; 0.89901578244]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.2855483205° = 154°17'8″ = 0.44988029836 rad
∠ B' = β' = 121.8211368525° = 121°49'17″ = 1.01554086735 rad
∠ C' = γ' = 83.89331482701° = 83°53'35″ = 1.67773809964 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 = 2.4 ; ; b = 4.7 ; ; c = 5.5 ; ;

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

p = a+b+c = 2.4+4.7+5.5 = 12.6 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.6 }{ 2 } = 6.3 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.3 * (6.3-2.4)(6.3-4.7)(6.3-5.5) } ; ; T = sqrt{ 31.45 } = 5.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.61 }{ 2.4 } = 4.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.61 }{ 4.7 } = 2.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.61 }{ 5.5 } = 2.04 ; ;

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{ 2.4**2-4.7**2-5.5**2 }{ 2 * 4.7 * 5.5 } ) = 25° 42'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.7**2-2.4**2-5.5**2 }{ 2 * 2.4 * 5.5 } ) = 58° 10'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.5**2-2.4**2-4.7**2 }{ 2 * 4.7 * 2.4 } ) = 96° 6'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.61 }{ 6.3 } = 0.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.4 }{ 2 * sin 25° 42'52" } = 2.77 ; ;




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