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=35; b=9.69771987616; c=42 and a=35; b=55.58330620008; c=42.

#1 Obtuse scalene triangle.

Sides: a = 35   b = 9.69771987616   c = 42

Area: T = 128.1565543252
Perimeter: p = 86.69771987616
Semiperimeter: s = 43.34985993808

Angle ∠ A = α = 39° = 0.68106784083 rad
Angle ∠ B = β = 10.04114908974° = 10°2'29″ = 0.1755257078 rad
Angle ∠ C = γ = 130.9598509103° = 130°57'31″ = 2.28656571673 rad

Height: ha = 7.32331739001
Height: hb = 26.43114564241
Height: hc = 6.10326449167

Median: ma = 24.95553167063
Median: mb = 38.35435015878
Median: mc = 14.78223486602

Inradius: r = 2.95663940954
Circumradius: R = 27.80877752587

Vertex coordinates: A[42; 0] B[0; 0] C[34.4643861145; 6.10326449167]
Centroid: CG[25.4887953715; 2.03442149722]
Coordinates of the circumscribed circle: U[21; -18.22883396072]
Coordinates of the inscribed circle: I[33.65114006192; 2.95663940954]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141° = 0.68106784083 rad
∠ B' = β' = 169.9598509103° = 169°57'31″ = 0.1755257078 rad
∠ C' = γ' = 49.04114908974° = 49°2'29″ = 2.28656571673 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 = 35 ; ; b = 9.7 ; ; c = 42 ; ;

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

p = a+b+c = 35+9.7+42 = 86.7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 86.7 }{ 2 } = 43.35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 43.35 * (43.35-35)(43.35-9.7)(43.35-42) } ; ; T = sqrt{ 16423.84 } = 128.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 128.16 }{ 35 } = 7.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 128.16 }{ 9.7 } = 26.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 128.16 }{ 42 } = 6.1 ; ;

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{ 35**2-9.7**2-42**2 }{ 2 * 9.7 * 42 } ) = 39° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.7**2-35**2-42**2 }{ 2 * 35 * 42 } ) = 10° 2'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 42**2-35**2-9.7**2 }{ 2 * 9.7 * 35 } ) = 130° 57'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 128.16 }{ 43.35 } = 2.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 35 }{ 2 * sin 39° } = 27.81 ; ;





#2 Obtuse scalene triangle.

Sides: a = 35   b = 55.58330620008   c = 42

Area: T = 734.5710640596
Perimeter: p = 132.5833062001
Semiperimeter: s = 66.29215310004

Angle ∠ A = α = 39° = 0.68106784083 rad
Angle ∠ B = β = 91.95985091026° = 91°57'31″ = 1.60549787591 rad
Angle ∠ C = γ = 49.04114908974° = 49°2'29″ = 0.85659354862 rad

Height: ha = 41.97554651769
Height: hb = 26.43114564241
Height: hc = 34.98795543141

Median: ma = 46.04987610115
Median: mb = 26.87224915974
Median: mc = 41.42875076573

Inradius: r = 11.08109122902
Circumradius: R = 27.80877752587

Vertex coordinates: A[42; 0] B[0; 0] C[-1.19661521593; 34.98795543141]
Centroid: CG[13.60112826136; 11.6659851438]
Coordinates of the circumscribed circle: U[21; 18.22883396072]
Coordinates of the inscribed circle: I[10.70884689996; 11.08109122902]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141° = 0.68106784083 rad
∠ B' = β' = 88.04114908974° = 88°2'29″ = 1.60549787591 rad
∠ C' = γ' = 130.9598509103° = 130°57'31″ = 0.85659354862 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 = 35 ; ; b = 55.58 ; ; c = 42 ; ;

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

p = a+b+c = 35+55.58+42 = 132.58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 132.58 }{ 2 } = 66.29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 66.29 * (66.29-35)(66.29-55.58)(66.29-42) } ; ; T = sqrt{ 539594.03 } = 734.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 734.57 }{ 35 } = 41.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 734.57 }{ 55.58 } = 26.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 734.57 }{ 42 } = 34.98 ; ;

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{ 35**2-55.58**2-42**2 }{ 2 * 55.58 * 42 } ) = 39° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 55.58**2-35**2-42**2 }{ 2 * 35 * 42 } ) = 91° 57'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 42**2-35**2-55.58**2 }{ 2 * 55.58 * 35 } ) = 49° 2'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 734.57 }{ 66.29 } = 11.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 35 }{ 2 * sin 39° } = 27.81 ; ; : Nr. 1




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