Triangle calculator

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

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 174   b = 138   c = 188

Area: T = 11486.34397129
Perimeter: p = 500
Semiperimeter: s = 250

Angle ∠ A = α = 62.31096326608° = 62°18'35″ = 1.08875082456 rad
Angle ∠ B = β = 44.60994683749° = 44°36'34″ = 0.77985821007 rad
Angle ∠ C = γ = 73.08108989643° = 73°4'51″ = 1.27655023072 rad

Height: ha = 132.0276893252
Height: hb = 166.4698691491
Height: hc = 122.1955103329

Median: ma = 140.0899257261
Median: mb = 167.4788356811
Median: mc = 125.7933481548

Inradius: r = 45.94553588516
Circumradius: R = 98.25327095845

Vertex coordinates: A[188; 0] B[0; 0] C[123.8722340425; 122.1955103329]
Centroid: CG[103.9577446808; 40.73217011096]
Coordinates of the circumscribed circle: U[94; 28.59436171321]
Coordinates of the inscribed circle: I[112; 45.94553588516]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.6990367339° = 117°41'25″ = 1.08875082456 rad
∠ B' = β' = 135.3910531625° = 135°23'26″ = 0.77985821007 rad
∠ C' = γ' = 106.9199101036° = 106°55'9″ = 1.27655023072 rad

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How did we calculate this triangle?

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

a = 174 ; ; b = 138 ; ; c = 188 ; ;


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 = 174 ; ; b = 138 ; ; c = 188 ; ; : Nr. 1

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

p = a+b+c = 174+138+188 = 500 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 500 }{ 2 } = 250 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 250 * (250-174)(250-138)(250-188) } ; ; T = sqrt{ 131936000 } = 11486.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11486.34 }{ 174 } = 132.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11486.34 }{ 138 } = 166.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11486.34 }{ 188 } = 122.2 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 138**2+188**2-174**2 }{ 2 * 138 * 188 } ) = 62° 18'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 174**2+188**2-138**2 }{ 2 * 174 * 188 } ) = 44° 36'34" ; ; gamma = 180° - alpha - beta = 180° - 62° 18'35" - 44° 36'34" = 73° 4'51" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11486.34 }{ 250 } = 45.95 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 174 }{ 2 * sin 62° 18'35" } = 98.25 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 138**2+2 * 188**2 - 174**2 } }{ 2 } = 140.089 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 188**2+2 * 174**2 - 138**2 } }{ 2 } = 167.478 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 138**2+2 * 174**2 - 188**2 } }{ 2 } = 125.793 ; ;
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