Triangle calculator

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

You have entered side b, c and angle γ.

Triangle has two solutions: a=9.70985809527; b=47; c=39 and a=70.86551453133; b=47; c=39.

#1 Obtuse scalene triangle.

Sides: a = 9.70985809527   b = 47   c = 39

Area: T = 117.5076787834
Perimeter: p = 95.70985809527
Semiperimeter: s = 47.85442904764

Angle ∠ A = α = 7.36663137074° = 7°21'59″ = 0.12985664279 rad
Angle ∠ B = β = 141.6343686293° = 141°38'1″ = 2.47219741575 rad
Angle ∠ C = γ = 31° = 0.54110520681 rad

Height: ha = 24.20767895208
Height: hb = 55.000288844
Height: hc = 6.02659891197

Median: ma = 42.91219547908
Median: mb = 15.9810559191
Median: mc = 27.77436974862

Inradius: r = 2.45655120693
Circumradius: R = 37.8611278515

Vertex coordinates: A[39; 0] B[0; 0] C[-7.61220955883; 6.02659891197]
Centroid: CG[10.46326348039; 2.00986630399]
Coordinates of the circumscribed circle: U[19.5; 32.45334499058]
Coordinates of the inscribed circle: I[0.85442904764; 2.45655120693]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.6343686293° = 172°38'1″ = 0.12985664279 rad
∠ B' = β' = 38.36663137074° = 38°21'59″ = 2.47219741575 rad
∠ C' = γ' = 149° = 0.54110520681 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 = 9.71 ; ; b = 47 ; ; c = 39 ; ;

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

p = a+b+c = 9.71+47+39 = 95.71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 95.71 }{ 2 } = 47.85 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 47.85 * (47.85-9.71)(47.85-47)(47.85-39) } ; ; T = sqrt{ 13807.85 } = 117.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 117.51 }{ 9.71 } = 24.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 117.51 }{ 47 } = 5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 117.51 }{ 39 } = 6.03 ; ;

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{ 9.71**2-47**2-39**2 }{ 2 * 47 * 39 } ) = 7° 21'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 47**2-9.71**2-39**2 }{ 2 * 9.71 * 39 } ) = 141° 38'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 39**2-9.71**2-47**2 }{ 2 * 47 * 9.71 } ) = 31° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 117.51 }{ 47.85 } = 2.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9.71 }{ 2 * sin 7° 21'59" } = 37.86 ; ;





#2 Obtuse scalene triangle.

Sides: a = 70.86551453133   b = 47   c = 39

Area: T = 857.7098828479
Perimeter: p = 156.8655145313
Semiperimeter: s = 78.43325726566

Angle ∠ A = α = 110.6343686293° = 110°38'1″ = 1.93109220894 rad
Angle ∠ B = β = 38.36663137074° = 38°21'59″ = 0.6769618496 rad
Angle ∠ C = γ = 31° = 0.54110520681 rad

Height: ha = 24.20767895208
Height: hb = 36.49882480204
Height: hc = 43.98550681271

Median: ma = 24.68987179686
Median: mb = 52.14657995445
Median: mc = 56.87986815084

Inradius: r = 10.93656202331
Circumradius: R = 37.8611278515

Vertex coordinates: A[39; 0] B[0; 0] C[55.56224207727; 43.98550681271]
Centroid: CG[31.52108069242; 14.66216893757]
Coordinates of the circumscribed circle: U[19.5; 32.45334499058]
Coordinates of the inscribed circle: I[31.43325726566; 10.93656202331]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 69.36663137074° = 69°21'59″ = 1.93109220894 rad
∠ B' = β' = 141.6343686293° = 141°38'1″ = 0.6769618496 rad
∠ C' = γ' = 149° = 0.54110520681 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 = 70.87 ; ; b = 47 ; ; c = 39 ; ;

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

p = a+b+c = 70.87+47+39 = 156.87 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 156.87 }{ 2 } = 78.43 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 78.43 * (78.43-70.87)(78.43-47)(78.43-39) } ; ; T = sqrt{ 735664.43 } = 857.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 857.71 }{ 70.87 } = 24.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 857.71 }{ 47 } = 36.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 857.71 }{ 39 } = 43.99 ; ;

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{ 70.87**2-47**2-39**2 }{ 2 * 47 * 39 } ) = 110° 38'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 47**2-70.87**2-39**2 }{ 2 * 70.87 * 39 } ) = 38° 21'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 39**2-70.87**2-47**2 }{ 2 * 47 * 70.87 } ) = 31° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 857.71 }{ 78.43 } = 10.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 70.87 }{ 2 * sin 110° 38'1" } = 37.86 ; ;




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