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=25.3; b=23.61881257376; c=42.1 and a=25.3; b=47.94328390119; c=42.1.

#1 Obtuse scalene triangle.

Sides: a = 25.3   b = 23.61881257376   c = 42.1

Area: T = 261.9822158372
Perimeter: p = 91.01881257376
Semiperimeter: s = 45.50990628688

Angle ∠ A = α = 31.8° = 31°48' = 0.55550147021 rad
Angle ∠ B = β = 29.46771998726° = 29°28'2″ = 0.51442996591 rad
Angle ∠ C = γ = 118.7332800127° = 118°43'58″ = 2.07222782923 rad

Height: ha = 20.71100520452
Height: hb = 22.18548389904
Height: hc = 12.44657082362

Median: ma = 31.70331612253
Median: mb = 32.66218437043
Median: mc = 12.48440070361

Inradius: r = 5.75767029918
Circumradius: R = 24.0065808662

Vertex coordinates: A[42.1; 0] B[0; 0] C[22.02771275136; 12.44657082362]
Centroid: CG[21.37657091712; 4.14985694121]
Coordinates of the circumscribed circle: U[21.05; -11.5440205783]
Coordinates of the inscribed circle: I[21.89109371312; 5.75767029918]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.2° = 148°12' = 0.55550147021 rad
∠ B' = β' = 150.5332800127° = 150°31'58″ = 0.51442996591 rad
∠ C' = γ' = 61.26771998726° = 61°16'2″ = 2.07222782923 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 = 25.3 ; ; b = 23.62 ; ; c = 42.1 ; ;

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

p = a+b+c = 25.3+23.62+42.1 = 91.02 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 91.02 }{ 2 } = 45.51 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 45.51 * (45.51-25.3)(45.51-23.62)(45.51-42.1) } ; ; T = sqrt{ 68634.65 } = 261.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 261.98 }{ 25.3 } = 20.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 261.98 }{ 23.62 } = 22.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 261.98 }{ 42.1 } = 12.45 ; ;

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{ 25.3**2-23.62**2-42.1**2 }{ 2 * 23.62 * 42.1 } ) = 31° 48' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23.62**2-25.3**2-42.1**2 }{ 2 * 25.3 * 42.1 } ) = 29° 28'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 42.1**2-25.3**2-23.62**2 }{ 2 * 23.62 * 25.3 } ) = 118° 43'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 261.98 }{ 45.51 } = 5.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25.3 }{ 2 * sin 31° 48' } = 24.01 ; ;





#2 Acute scalene triangle.

Sides: a = 25.3   b = 47.94328390119   c = 42.1

Area: T = 531.8022082111
Perimeter: p = 115.3432839012
Semiperimeter: s = 57.6711419506

Angle ∠ A = α = 31.8° = 31°48' = 0.55550147021 rad
Angle ∠ B = β = 86.93328001274° = 86°55'58″ = 1.51772635902 rad
Angle ∠ C = γ = 61.26771998726° = 61°16'2″ = 1.06993143613 rad

Height: ha = 42.04396902855
Height: hb = 22.18548389904
Height: hc = 25.26437568699

Median: ma = 43.30663552641
Median: mb = 25.13220720767
Median: mc = 32.03443628977

Inradius: r = 9.22112414168
Circumradius: R = 24.0065808662

Vertex coordinates: A[42.1; 0] B[0; 0] C[1.35437314427; 25.26437568699]
Centroid: CG[14.48545771476; 8.421125229]
Coordinates of the circumscribed circle: U[21.05; 11.5440205783]
Coordinates of the inscribed circle: I[9.7298580494; 9.22112414168]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.2° = 148°12' = 0.55550147021 rad
∠ B' = β' = 93.06771998726° = 93°4'2″ = 1.51772635902 rad
∠ C' = γ' = 118.7332800127° = 118°43'58″ = 1.06993143613 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 = 25.3 ; ; b = 47.94 ; ; c = 42.1 ; ;

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

p = a+b+c = 25.3+47.94+42.1 = 115.34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 115.34 }{ 2 } = 57.67 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 57.67 * (57.67-25.3)(57.67-47.94)(57.67-42.1) } ; ; T = sqrt{ 282813.45 } = 531.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 531.8 }{ 25.3 } = 42.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 531.8 }{ 47.94 } = 22.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 531.8 }{ 42.1 } = 25.26 ; ;

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{ 25.3**2-47.94**2-42.1**2 }{ 2 * 47.94 * 42.1 } ) = 31° 48' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 47.94**2-25.3**2-42.1**2 }{ 2 * 25.3 * 42.1 } ) = 86° 55'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 42.1**2-25.3**2-47.94**2 }{ 2 * 47.94 * 25.3 } ) = 61° 16'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 531.8 }{ 57.67 } = 9.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25.3 }{ 2 * sin 31° 48' } = 24.01 ; ; : Nr. 1




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