Triangle calculator

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

You have entered side a, b and angle β.

Triangle has two solutions: a=24.15; b=12.5; c=12.50220682648 and a=24.15; b=12.5; c=34.1522149145.

#1 Obtuse scalene triangle.

Sides: a = 24.15   b = 12.5   c = 12.50220682648

Area: T = 39.0721963444
Perimeter: p = 49.15220682648
Semiperimeter: s = 24.57660341324

Angle ∠ A = α = 149.9977459766° = 149°59'51″ = 2.61879495425 rad
Angle ∠ B = β = 15° = 0.26217993878 rad
Angle ∠ C = γ = 15.00325402344° = 15°9″ = 0.26218437233 rad

Height: ha = 3.23657733701
Height: hb = 6.2521514151
Height: hc = 6.25504799392

Median: ma = 3.23657735472
Median: mb = 18.18551479359
Median: mc = 18.18440815626

Inradius: r = 1.59898400545
Circumradius: R = 24.14881456572

Vertex coordinates: A[12.50220682648; 0] B[0; 0] C[23.32771087049; 6.25504799392]
Centroid: CG[11.94330589899; 2.08334933131]
Coordinates of the circumscribed circle: U[6.25110341324; 23.32550404278]
Coordinates of the inscribed circle: I[12.07660341324; 1.59898400545]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 30.00325402344° = 30°9″ = 2.61879495425 rad
∠ B' = β' = 165° = 0.26217993878 rad
∠ C' = γ' = 164.9977459766° = 164°59'51″ = 0.26218437233 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 = 24.15 ; ; b = 12.5 ; ; c = 12.5 ; ;

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

p = a+b+c = 24.15+12.5+12.5 = 49.15 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49.15 }{ 2 } = 24.58 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.58 * (24.58-24.15)(24.58-12.5)(24.58-12.5) } ; ; T = sqrt{ 1526.62 } = 39.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.07 }{ 24.15 } = 3.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.07 }{ 12.5 } = 6.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.07 }{ 12.5 } = 6.25 ; ;

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{ 24.15**2-12.5**2-12.5**2 }{ 2 * 12.5 * 12.5 } ) = 149° 59'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12.5**2-24.15**2-12.5**2 }{ 2 * 24.15 * 12.5 } ) = 15° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12.5**2-24.15**2-12.5**2 }{ 2 * 12.5 * 24.15 } ) = 15° 9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.07 }{ 24.58 } = 1.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24.15 }{ 2 * sin 149° 59'51" } = 24.15 ; ;





#2 Obtuse scalene triangle.

Sides: a = 24.15   b = 12.5   c = 34.1522149145

Area: T = 106.7343661556
Perimeter: p = 70.8022149145
Semiperimeter: s = 35.40110745725

Angle ∠ A = α = 30.00325402344° = 30°9″ = 0.52436431111 rad
Angle ∠ B = β = 15° = 0.26217993878 rad
Angle ∠ C = γ = 134.9977459766° = 134°59'51″ = 2.35661501547 rad

Height: ha = 8.83992266299
Height: hb = 17.0777385849
Height: hc = 6.25504799392

Median: ma = 22.7054713621
Median: mb = 28.90990538692
Median: mc = 8.84399053838

Inradius: r = 3.01549836649
Circumradius: R = 24.14881456572

Vertex coordinates: A[34.1522149145; 0] B[0; 0] C[23.32771087049; 6.25504799392]
Centroid: CG[19.16597526166; 2.08334933131]
Coordinates of the circumscribed circle: U[17.07660745725; -17.07545604886]
Coordinates of the inscribed circle: I[22.90110745725; 3.01549836649]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.9977459766° = 149°59'51″ = 0.52436431111 rad
∠ B' = β' = 165° = 0.26217993878 rad
∠ C' = γ' = 45.00325402344° = 45°9″ = 2.35661501547 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 = 24.15 ; ; b = 12.5 ; ; c = 34.15 ; ;

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

p = a+b+c = 24.15+12.5+34.15 = 70.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70.8 }{ 2 } = 35.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.4 * (35.4-24.15)(35.4-12.5)(35.4-34.15) } ; ; T = sqrt{ 11392.07 } = 106.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 106.73 }{ 24.15 } = 8.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 106.73 }{ 12.5 } = 17.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 106.73 }{ 34.15 } = 6.25 ; ;

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{ 24.15**2-12.5**2-34.15**2 }{ 2 * 12.5 * 34.15 } ) = 30° 9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12.5**2-24.15**2-34.15**2 }{ 2 * 24.15 * 34.15 } ) = 15° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 34.15**2-24.15**2-12.5**2 }{ 2 * 12.5 * 24.15 } ) = 134° 59'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 106.73 }{ 35.4 } = 3.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24.15 }{ 2 * sin 30° 9" } = 24.15 ; ;




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