Triangle calculator

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

You have entered side a, c and angle α.

Triangle has two solutions: a=6.3; b=3.30110726037; c=9.3 and a=6.3; b=14.17772101429; c=9.3.

#1 Obtuse scalene triangle.

Sides: a = 6.3   b = 3.30110726037   c = 9.3

Area: T = 5.25500049615
Perimeter: p = 18.90110726037
Semiperimeter: s = 9.45105363019

Angle ∠ A = α = 20° = 0.34990658504 rad
Angle ∠ B = β = 10.32438433776° = 10°19'26″ = 0.18801850584 rad
Angle ∠ C = γ = 149.6766156622° = 149°40'34″ = 2.61223417448 rad

Height: ha = 1.66766682417
Height: hb = 3.18107873329
Height: hc = 1.12990333251

Median: ma = 6.22766395566
Median: mb = 7.77695385909
Median: mc = 1.91659958684

Inradius: r = 0.55655245537
Circumradius: R = 9.21099838605

Vertex coordinates: A[9.3; 0] B[0; 0] C[6.19880064336; 1.12990333251]
Centroid: CG[5.16660021445; 0.37663444417]
Coordinates of the circumscribed circle: U[4.65; -7.95499246984]
Coordinates of the inscribed circle: I[6.14994636981; 0.55655245537]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160° = 0.34990658504 rad
∠ B' = β' = 169.6766156622° = 169°40'34″ = 0.18801850584 rad
∠ C' = γ' = 30.32438433776° = 30°19'26″ = 2.61223417448 rad




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 = 6.3 ; ; b = 3.3 ; ; c = 9.3 ; ;

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

p = a+b+c = 6.3+3.3+9.3 = 18.9 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18.9 }{ 2 } = 9.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.45 * (9.45-6.3)(9.45-3.3)(9.45-9.3) } ; ; T = sqrt{ 27.56 } = 5.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.25 }{ 6.3 } = 1.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.25 }{ 3.3 } = 3.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.25 }{ 9.3 } = 1.13 ; ;

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{ 6.3**2-3.3**2-9.3**2 }{ 2 * 3.3 * 9.3 } ) = 20° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3.3**2-6.3**2-9.3**2 }{ 2 * 6.3 * 9.3 } ) = 10° 19'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.3**2-6.3**2-3.3**2 }{ 2 * 3.3 * 6.3 } ) = 149° 40'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.25 }{ 9.45 } = 0.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.3 }{ 2 * sin 20° } = 9.21 ; ;





#2 Obtuse scalene triangle.

Sides: a = 6.3   b = 14.17772101429   c = 9.3

Area: T = 22.54773452194
Perimeter: p = 29.77772101429
Semiperimeter: s = 14.88986050714

Angle ∠ A = α = 20° = 0.34990658504 rad
Angle ∠ B = β = 129.6766156622° = 129°40'34″ = 2.26332758944 rad
Angle ∠ C = γ = 30.32438433776° = 30°19'26″ = 0.52992509088 rad

Height: ha = 7.15878873712
Height: hb = 3.18107873329
Height: hc = 4.8498891445

Median: ma = 11.56880224636
Median: mb = 3.58435287275
Median: mc = 9.93657507878

Inradius: r = 1.51444028007
Circumradius: R = 9.21099838605

Vertex coordinates: A[9.3; 0] B[0; 0] C[-4.02222197546; 4.8498891445]
Centroid: CG[1.75992600818; 1.61662971483]
Coordinates of the circumscribed circle: U[4.65; 7.95499246984]
Coordinates of the inscribed circle: I[0.71113949286; 1.51444028007]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160° = 0.34990658504 rad
∠ B' = β' = 50.32438433776° = 50°19'26″ = 2.26332758944 rad
∠ C' = γ' = 149.6766156622° = 149°40'34″ = 0.52992509088 rad

Calculate another triangle

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 = 6.3 ; ; b = 14.18 ; ; c = 9.3 ; ;

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

p = a+b+c = 6.3+14.18+9.3 = 29.78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29.78 }{ 2 } = 14.89 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.89 * (14.89-6.3)(14.89-14.18)(14.89-9.3) } ; ; T = sqrt{ 508.38 } = 22.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.55 }{ 6.3 } = 7.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.55 }{ 14.18 } = 3.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.55 }{ 9.3 } = 4.85 ; ;

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{ 6.3**2-14.18**2-9.3**2 }{ 2 * 14.18 * 9.3 } ) = 20° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14.18**2-6.3**2-9.3**2 }{ 2 * 6.3 * 9.3 } ) = 129° 40'34" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.3**2-6.3**2-14.18**2 }{ 2 * 14.18 * 6.3 } ) = 30° 19'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.55 }{ 14.89 } = 1.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.3 }{ 2 * sin 20° } = 9.21 ; ; : Nr. 1




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