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=49; b=41; c=88.0000511955 and a=49; b=41; c=89.99994240538.

#1 Obtuse scalene triangle.

Sides: a = 49   b = 41   c = 88.0000511955

Area: T = 0.64114114599
Perimeter: p = 988.0000511955
Semiperimeter: s = 499.0000255978

Angle ∠ A = α = 179.7765914463° = 179°46'33″ = 3.13876816232 rad
Angle ∠ B = β = 0.18875° = 0°11'15″ = 0.00332724923 rad
Angle ∠ C = γ = 0.03765855372° = 0°2'12″ = 0.00106385381 rad

Height: ha = 0.02661800596
Height: hb = 0.03112883639
Height: hc = 0.16603518388

Median: ma = 16.55000124111
Median: mb = 28.55000071854
Median: mc = 454.9999977246

Inradius: r = 0.0133090023
Circumradius: R = 6264.354974116

Vertex coordinates: A[88.0000511955; 0] B[0; 0] C[498.9997376247; 0.16603518388]
Centroid: CG[198.9999296067; 0.05334506129]
Coordinates of the circumscribed circle: U[44.0000255978; 6264.348846401]
Coordinates of the inscribed circle: I[88.0000255978; 0.0133090023]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 0.22440855372° = 0°13'27″ = 3.13876816232 rad
∠ B' = β' = 179.81325° = 179°48'45″ = 0.00332724923 rad
∠ C' = γ' = 179.9633414463° = 179°57'48″ = 0.00106385381 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 = 49 ; ; b = 41 ; ; c = 8 ; ;

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

p = a+b+c = 49+41+8 = 98 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 98 }{ 2 } = 49 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 49 * (49-49)(49-41)(49-8) } ; ; T = sqrt{ 0.41 } = 0.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.64 }{ 49 } = 0.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.64 }{ 41 } = 0.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.64 }{ 8 } = 0.16 ; ;

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{ 49**2-41**2-8**2 }{ 2 * 41 * 8 } ) = 179° 46'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 41**2-49**2-8**2 }{ 2 * 49 * 8 } ) = 0° 11'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8**2-49**2-41**2 }{ 2 * 41 * 49 } ) = 0° 2'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.64 }{ 49 } = 0.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 49 }{ 2 * sin 179° 46'33" } = 6264.35 ; ;





#2 Obtuse scalene triangle.

Sides: a = 49   b = 41   c = 89.99994240538

Area: T = 7.21657865699
Perimeter: p = 179.9999424054
Semiperimeter: s = 909.9997120269

Angle ∠ A = α = 0.22440855372° = 0°13'27″ = 0.00439110304 rad
Angle ∠ B = β = 0.18875° = 0°11'15″ = 0.00332724923 rad
Angle ∠ C = γ = 179.5888414463° = 179°35'18″ = 3.13444091308 rad

Height: ha = 0.29545219008
Height: hb = 0.35219895888
Height: hc = 0.16603518388

Median: ma = 65.54996043119
Median: mb = 69.54996270854
Median: mc = 4.0033238376

Inradius: r = 0.08801756629
Circumradius: R = 6264.354974116

Vertex coordinates: A[89.99994240538; 0] B[0; 0] C[498.9997376247; 0.16603518388]
Centroid: CG[46.33330538928; 0.05334506129]
Coordinates of the circumscribed circle: U[454.9997120269; -6264.188811217]
Coordinates of the inscribed circle: I[498.9997120269; 0.08801756629]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.7765914463° = 179°46'33″ = 0.00439110304 rad
∠ B' = β' = 179.81325° = 179°48'45″ = 0.00332724923 rad
∠ C' = γ' = 0.41215855372° = 0°24'42″ = 3.13444091308 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 = 49 ; ; b = 41 ; ; c = 90 ; ;

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

p = a+b+c = 49+41+90 = 180 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 180 }{ 2 } = 90 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 90 * (90-49)(90-41)(90-90) } ; ; T = sqrt{ 52.07 } = 7.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.22 }{ 49 } = 0.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.22 }{ 41 } = 0.35 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.22 }{ 90 } = 0.16 ; ;

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{ 49**2-41**2-90**2 }{ 2 * 41 * 90 } ) = 0° 13'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 41**2-49**2-90**2 }{ 2 * 49 * 90 } ) = 0° 11'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 90**2-49**2-41**2 }{ 2 * 41 * 49 } ) = 179° 35'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.22 }{ 90 } = 0.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 49 }{ 2 * sin 0° 13'27" } = 6264.35 ; ;




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