Triangle calculator

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

You have entered side a, height ha and height hb.

Triangle has two solutions: a=6.6; b=4.4; c=9.33435952167 and a=6.6; b=4.4; c=6.22328611049.

#1 Obtuse scalene triangle.

Sides: a = 6.6   b = 4.4   c = 9.33435952167

Area: T = 13.2
Perimeter: p = 20.33435952167
Semiperimeter: s = 10.16767976084

Angle ∠ A = α = 40.00438517017° = 40°14″ = 0.69881989257 rad
Angle ∠ B = β = 25.37661709696° = 25°22'34″ = 0.4432897735 rad
Angle ∠ C = γ = 114.6219977329° = 114°37'12″ = 22.0004959929 rad

Height: ha = 4
Height: hb = 6
Height: hc = 2.82884920641

Median: ma = 6.50875340825
Median: mb = 7.77880460165
Median: mc = 3.11114305524

Inradius: r = 1.29883439337
Circumradius: R = 5.13334773692

Vertex coordinates: A[9.33435952167; 0] B[0; 0] C[5.96331898044; 2.82884920641]
Centroid: CG[5.09989283404; 0.9432830688]
Coordinates of the circumscribed circle: U[4.66767976084; -2.13985953293]
Coordinates of the inscribed circle: I[5.76767976084; 1.29883439337]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.9966148298° = 139°59'46″ = 0.69881989257 rad
∠ B' = β' = 154.624382903° = 154°37'26″ = 0.4432897735 rad
∠ C' = γ' = 65.38800226713° = 65°22'48″ = 22.0004959929 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 = 6.6 ; ; b = 4.4 ; ; c = 9.33 ; ;

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

p = a+b+c = 6.6+4.4+9.33 = 20.33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20.33 }{ 2 } = 10.17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.17 * (10.17-6.6)(10.17-4.4)(10.17-9.33) } ; ; T = sqrt{ 174.24 } = 13.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.2 }{ 6.6 } = 4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.2 }{ 4.4 } = 6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.2 }{ 9.33 } = 2.83 ; ;

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{ 6.6**2-4.4**2-9.33**2 }{ 2 * 4.4 * 9.33 } ) = 40° 14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.4**2-6.6**2-9.33**2 }{ 2 * 6.6 * 9.33 } ) = 25° 22'34" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.33**2-6.6**2-4.4**2 }{ 2 * 4.4 * 6.6 } ) = 114° 37'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.2 }{ 10.17 } = 1.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.6 }{ 2 * sin 40° 14" } = 5.13 ; ;





#2 Acute scalene triangle.

Sides: a = 6.6   b = 4.4   c = 6.22328611049

Area: T = 13.2
Perimeter: p = 17.22328611049
Semiperimeter: s = 8.61114305524

Angle ∠ A = α = 74.62197130844° = 74°37'11″ = 1.30223596802 rad
Angle ∠ B = β = 400.0002642442° = 40°1″ = 0.69881363127 rad
Angle ∠ C = γ = 65.38800226713° = 65°22'48″ = 1.14110966606 rad

Height: ha = 4
Height: hb = 6
Height: hc = 4.24224215413

Median: ma = 4.261051642
Median: mb = 6.02551141205
Median: mc = 4.66767976084

Inradius: r = 1.53328463627
Circumradius: R = 3.42325736077

Vertex coordinates: A[6.22328611049; 0] B[0; 0] C[5.05658737589; 4.24224215413]
Centroid: CG[3.76595782879; 1.41441405138]
Coordinates of the circumscribed circle: U[3.11114305524; 1.42658366026]
Coordinates of the inscribed circle: I[4.21114305524; 1.53328463627]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105.3880286916° = 105°22'49″ = 1.30223596802 rad
∠ B' = β' = 1409.999735756° = 139°59'59″ = 0.69881363127 rad
∠ C' = γ' = 114.6219977329° = 114°37'12″ = 1.14110966606 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 = 6.6 ; ; b = 4.4 ; ; c = 6.22 ; ;

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

p = a+b+c = 6.6+4.4+6.22 = 17.22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.22 }{ 2 } = 8.61 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.61 * (8.61-6.6)(8.61-4.4)(8.61-6.22) } ; ; T = sqrt{ 174.24 } = 13.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.2 }{ 6.6 } = 4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.2 }{ 4.4 } = 6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.2 }{ 6.22 } = 4.24 ; ;

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{ 6.6**2-4.4**2-6.22**2 }{ 2 * 4.4 * 6.22 } ) = 74° 37'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.4**2-6.6**2-6.22**2 }{ 2 * 6.6 * 6.22 } ) = 40° 1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.22**2-6.6**2-4.4**2 }{ 2 * 4.4 * 6.6 } ) = 65° 22'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.2 }{ 8.61 } = 1.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.6 }{ 2 * sin 74° 37'11" } = 3.42 ; ;




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

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