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=22.42; b=16.8; c=6.23774731119 and a=22.42; b=16.8; c=35.33774509269.

#1 Obtuse scalene triangle.

Sides: a = 22.42   b = 16.8   c = 6.23774731119

Area: T = 26.19332697901
Perimeter: p = 45.45774731119
Semiperimeter: s = 22.7298736556

Angle ∠ A = α = 150.0055198799° = 150°19″ = 2.61880846142 rad
Angle ∠ B = β = 22° = 0.38439724354 rad
Angle ∠ C = γ = 7.99548012007° = 7°59'41″ = 0.1439535604 rad

Height: ha = 2.3376598554
Height: hb = 3.11882464036
Height: hc = 8.39986798244

Median: ma = 5.90883784079
Median: mb = 14.15499553148
Median: mc = 19.56332738133

Inradius: r = 1.15224296445
Circumradius: R = 22.42435241655

Vertex coordinates: A[6.23774731119; 0] B[0; 0] C[20.78774620194; 8.39986798244]
Centroid: CG[9.00883117104; 2.87995599415]
Coordinates of the circumscribed circle: U[3.1198736556; 22.20655830433]
Coordinates of the inscribed circle: I[5.9298736556; 1.15224296445]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 29.99548012007° = 29°59'41″ = 2.61880846142 rad
∠ B' = β' = 158° = 0.38439724354 rad
∠ C' = γ' = 172.0055198799° = 172°19″ = 0.1439535604 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 = 22.42 ; ; b = 16.8 ; ; c = 6.24 ; ;

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

p = a+b+c = 22.42+16.8+6.24 = 45.46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45.46 }{ 2 } = 22.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.73 * (22.73-22.42)(22.73-16.8)(22.73-6.24) } ; ; T = sqrt{ 686.09 } = 26.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.19 }{ 22.42 } = 2.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.19 }{ 16.8 } = 3.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.19 }{ 6.24 } = 8.4 ; ;

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{ 22.42**2-16.8**2-6.24**2 }{ 2 * 16.8 * 6.24 } ) = 150° 19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16.8**2-22.42**2-6.24**2 }{ 2 * 22.42 * 6.24 } ) = 22° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.24**2-22.42**2-16.8**2 }{ 2 * 16.8 * 22.42 } ) = 7° 59'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.19 }{ 22.73 } = 1.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22.42 }{ 2 * sin 150° 19" } = 22.42 ; ;





#2 Obtuse scalene triangle.

Sides: a = 22.42   b = 16.8   c = 35.33774509269

Area: T = 148.3943968072
Perimeter: p = 74.55774509269
Semiperimeter: s = 37.27987254634

Angle ∠ A = α = 29.99548012007° = 29°59'41″ = 0.52435080394 rad
Angle ∠ B = β = 22° = 0.38439724354 rad
Angle ∠ C = γ = 128.0055198799° = 128°19″ = 2.23441121787 rad

Height: ha = 13.23876421117
Height: hb = 17.666594858
Height: hc = 8.39986798244

Median: ma = 25.29547350056
Median: mb = 28.37549170748
Median: mc = 8.95990368064

Inradius: r = 3.98106609863
Circumradius: R = 22.42435241655

Vertex coordinates: A[35.33774509269; 0] B[0; 0] C[20.78774620194; 8.39986798244]
Centroid: CG[18.70883043154; 2.87995599415]
Coordinates of the circumscribed circle: U[17.66987254634; -13.80769032189]
Coordinates of the inscribed circle: I[20.47987254634; 3.98106609863]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.0055198799° = 150°19″ = 0.52435080394 rad
∠ B' = β' = 158° = 0.38439724354 rad
∠ C' = γ' = 51.99548012007° = 51°59'41″ = 2.23441121787 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 = 22.42 ; ; b = 16.8 ; ; c = 35.34 ; ;

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

p = a+b+c = 22.42+16.8+35.34 = 74.56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74.56 }{ 2 } = 37.28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.28 * (37.28-22.42)(37.28-16.8)(37.28-35.34) } ; ; T = sqrt{ 22020.77 } = 148.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 148.39 }{ 22.42 } = 13.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 148.39 }{ 16.8 } = 17.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 148.39 }{ 35.34 } = 8.4 ; ;

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{ 22.42**2-16.8**2-35.34**2 }{ 2 * 16.8 * 35.34 } ) = 29° 59'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16.8**2-22.42**2-35.34**2 }{ 2 * 22.42 * 35.34 } ) = 22° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 35.34**2-22.42**2-16.8**2 }{ 2 * 16.8 * 22.42 } ) = 128° 19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 148.39 }{ 37.28 } = 3.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22.42 }{ 2 * sin 29° 59'41" } = 22.42 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.