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=700; b=100.0769671742; c=800 and a=700; b=1498.956565149; c=800.

#1 Obtuse scalene triangle.

Sides: a = 700   b = 100.0769671742   c = 800

Area: T = 1396.952247159
Perimeter: p = 1600.076967174
Semiperimeter: s = 800.0354835871

Angle ∠ A = α = 2° = 0.0354906585 rad
Angle ∠ B = β = 0.28658564745° = 0°17'9″ = 0.00549891367 rad
Angle ∠ C = γ = 177.7144143526° = 177°42'51″ = 3.10216969319 rad

Height: ha = 3.9911292776
Height: hb = 27.9219597362
Height: hc = 3.4922381179

Median: ma = 450.0087743935
Median: mb = 749.9987676796
Median: mc = 300.0121615777

Inradius: r = 1.74661145552
Circumradius: R = 10028.79879218

Vertex coordinates: A[800; 0] B[0; 0] C[699.9911287998; 3.4922381179]
Centroid: CG[499.9977096; 1.16441270597]
Coordinates of the circumscribed circle: U[400; -10020.81877189]
Coordinates of the inscribed circle: I[699.9655164129; 1.74661145552]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 178° = 0.0354906585 rad
∠ B' = β' = 179.7144143526° = 179°42'51″ = 0.00549891367 rad
∠ C' = γ' = 2.28658564745° = 2°17'9″ = 3.10216969319 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 = 700 ; ; b = 100.07 ; ; c = 800 ; ;

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

p = a+b+c = 700+100.07+800 = 1600.07 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1600.07 }{ 2 } = 800.03 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 800.03 * (800.03-700)(800.03-100.07)(800.03-800) } ; ; T = sqrt{ 1951476.21 } = 1396.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1396.95 }{ 700 } = 3.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1396.95 }{ 100.07 } = 27.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1396.95 }{ 800 } = 3.49 ; ;

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{ 700**2-100.07**2-800**2 }{ 2 * 100.07 * 800 } ) = 2° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 100.07**2-700**2-800**2 }{ 2 * 700 * 800 } ) = 0° 17'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 800**2-700**2-100.07**2 }{ 2 * 100.07 * 700 } ) = 177° 42'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1396.95 }{ 800.03 } = 1.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 700 }{ 2 * sin 2° } = 10028.8 ; ;





#2 Obtuse scalene triangle.

Sides: a = 700   b = 1498.956565149   c = 800

Area: T = 20925.11991265
Perimeter: p = 2998.956565149
Semiperimeter: s = 1499.478782574

Angle ∠ A = α = 2° = 0.0354906585 rad
Angle ∠ B = β = 175.7144143526° = 175°42'51″ = 3.06767903468 rad
Angle ∠ C = γ = 2.28658564745° = 2°17'9″ = 0.04398957217 rad

Height: ha = 59.78660546472
Height: hb = 27.9219597362
Height: hc = 52.31327978163

Median: ma = 1149.319893857
Median: mb = 57.29773709474
Median: mc = 1099.288796162

Inradius: r = 13.9554937357
Circumradius: R = 10028.79879217

Vertex coordinates: A[800; 0] B[0; 0] C[-698.0432528206; 52.31327978163]
Centroid: CG[33.98658239312; 17.43875992721]
Coordinates of the circumscribed circle: U[400; 10020.81877189]
Coordinates of the inscribed circle: I[0.52221742556; 13.9554937357]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 178° = 0.0354906585 rad
∠ B' = β' = 4.28658564745° = 4°17'9″ = 3.06767903468 rad
∠ C' = γ' = 177.7144143526° = 177°42'51″ = 0.04398957217 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 = 700 ; ; b = 1498.96 ; ; c = 800 ; ;

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

p = a+b+c = 700+1498.96+800 = 2998.96 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2998.96 }{ 2 } = 1499.48 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1499.48 * (1499.48-700)(1499.48-1498.96)(1499.48-800) } ; ; T = sqrt{ 437860610.46 } = 20925.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20925.12 }{ 700 } = 59.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20925.12 }{ 1498.96 } = 27.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20925.12 }{ 800 } = 52.31 ; ;

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{ 700**2-1498.96**2-800**2 }{ 2 * 1498.96 * 800 } ) = 2° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1498.96**2-700**2-800**2 }{ 2 * 700 * 800 } ) = 175° 42'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 800**2-700**2-1498.96**2 }{ 2 * 1498.96 * 700 } ) = 2° 17'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20925.12 }{ 1499.48 } = 13.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 700 }{ 2 * sin 2° } = 10028.8 ; ; : Nr. 1




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