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=63; b=103.0022383815; c=160 and a=63; b=210.0054848419; c=160.

#1 Obtuse scalene triangle.

Sides: a = 63   b = 103.0022383815   c = 160

Area: T = 1713.232198219
Perimeter: p = 326.0022383816
Semiperimeter: s = 163.0011191908

Angle ∠ A = α = 12° = 0.20994395102 rad
Angle ∠ B = β = 19.87224253972° = 19°52'21″ = 0.34768392535 rad
Angle ∠ C = γ = 148.1287574603° = 148°7'39″ = 2.58553138898 rad

Height: ha = 54.38883168948
Height: hb = 33.26658705308
Height: hc = 21.41553997773

Median: ma = 130.8154737457
Median: mb = 110.1465936067
Median: mc = 29.82202202513

Inradius: r = 10.51105488011
Circumradius: R = 151.5076631859

Vertex coordinates: A[160; 0] B[0; 0] C[59.2488465401; 21.41553997773]
Centroid: CG[73.08328218003; 7.13884665924]
Coordinates of the circumscribed circle: U[80; -128.6633357244]
Coordinates of the inscribed circle: I[59.99988080923; 10.51105488011]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168° = 0.20994395102 rad
∠ B' = β' = 160.1287574603° = 160°7'39″ = 0.34768392535 rad
∠ C' = γ' = 31.87224253972° = 31°52'21″ = 2.58553138898 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 = 63 ; ; b = 103 ; ; c = 160 ; ;

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

p = a+b+c = 63+103+160 = 326 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 326 }{ 2 } = 163 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 163 * (163-63)(163-103)(163-160) } ; ; T = sqrt{ 2935163.82 } = 1713.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1713.23 }{ 63 } = 54.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1713.23 }{ 103 } = 33.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1713.23 }{ 160 } = 21.42 ; ;

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{ 63**2-103**2-160**2 }{ 2 * 103 * 160 } ) = 12° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 103**2-63**2-160**2 }{ 2 * 63 * 160 } ) = 19° 52'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 160**2-63**2-103**2 }{ 2 * 103 * 63 } ) = 148° 7'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1713.23 }{ 163 } = 10.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 63 }{ 2 * sin 12° } = 151.51 ; ;





#2 Obtuse scalene triangle.

Sides: a = 63   b = 210.0054848419   c = 160

Area: T = 3492.997704918
Perimeter: p = 433.0054848419
Semiperimeter: s = 216.502242421

Angle ∠ A = α = 12° = 0.20994395102 rad
Angle ∠ B = β = 136.1287574603° = 136°7'39″ = 2.37658743796 rad
Angle ∠ C = γ = 31.87224253972° = 31°52'21″ = 0.55662787638 rad

Height: ha = 110.8898795212
Height: hb = 33.26658705308
Height: hc = 43.66224631148

Median: ma = 184.0087522074
Median: mb = 61.3110610094
Median: mc = 132.7998788322

Inradius: r = 16.1343754908
Circumradius: R = 151.5076631859

Vertex coordinates: A[160; 0] B[0; 0] C[-45.41657386238; 43.66224631148]
Centroid: CG[38.19547537921; 14.55441543716]
Coordinates of the circumscribed circle: U[80; 128.6633357244]
Coordinates of the inscribed circle: I[6.49875757903; 16.1343754908]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168° = 0.20994395102 rad
∠ B' = β' = 43.87224253972° = 43°52'21″ = 2.37658743796 rad
∠ C' = γ' = 148.1287574603° = 148°7'39″ = 0.55662787638 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 = 63 ; ; b = 210 ; ; c = 160 ; ;

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

p = a+b+c = 63+210+160 = 433 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 433 }{ 2 } = 216.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 216.5 * (216.5-63)(216.5-210)(216.5-160) } ; ; T = sqrt{ 12201028.39 } = 3493 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3493 }{ 63 } = 110.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3493 }{ 210 } = 33.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3493 }{ 160 } = 43.66 ; ;

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{ 63**2-210**2-160**2 }{ 2 * 210 * 160 } ) = 12° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 210**2-63**2-160**2 }{ 2 * 63 * 160 } ) = 136° 7'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 160**2-63**2-210**2 }{ 2 * 210 * 63 } ) = 31° 52'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3493 }{ 216.5 } = 16.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 63 }{ 2 * sin 12° } = 151.51 ; ; : Nr. 1




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