Triangle calculator

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

You have entered side a, b and height hb.

Triangle has two solutions: a=0.013; b=0.016; c=0.02441867732 and a=0.013; b=0.016; c=0.01662788206.

#1 Obtuse scalene triangle.

Sides: a = 0.013   b = 0.016   c = 0.02441867732

Area: T = 09.6E-5
Perimeter: p = 0.05331867732
Semiperimeter: s = 0.02765933866

Angle ∠ A = α = 29.74548812969° = 29°44'42″ = 0.51991461142 rad
Angle ∠ B = β = 37.6355253755° = 37°38'7″ = 0.65768590928 rad
Angle ∠ C = γ = 112.6219864948° = 112°37'11″ = 1.96655874465 rad

Height: ha = 0.01547692308
Height: hb = 0.012
Height: hc = 0.0087938223

Median: ma = 0.01994486503
Median: mb = 0.0187691806
Median: mc = 0.00881394103

Inradius: r = 0.00436099201
Circumradius: R = 0.01331011688

Vertex coordinates: A[0.02441867732; 0] B[0; 0] C[0.0110294883; 0.0087938223]
Centroid: CG[0.01114938854; 0.00326460743]
Coordinates of the circumscribed circle: U[0.01220933866; -0.00550389111]
Coordinates of the inscribed circle: I[0.01105933866; 0.00436099201]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.2555118703° = 150°15'18″ = 0.51991461142 rad
∠ B' = β' = 142.3654746245° = 142°21'53″ = 0.65768590928 rad
∠ C' = γ' = 67.3880135052° = 67°22'49″ = 1.96655874465 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 = 0.01 ; ; b = 0.02 ; ; c = 0.02 ; ;

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

p = a+b+c = 0.01+0.02+0.02 = 0.05 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.05 }{ 2 } = 0.03 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.03 * (0.03-0.01)(0.03-0.02)(0.03-0.02) } ; ; T = sqrt{ 0 } = 0 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0 }{ 0.01 } = 0.01 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0 }{ 0.02 } = 0.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0 }{ 0.02 } = 0.01 ; ;

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{ 0.01**2-0.02**2-0.02**2 }{ 2 * 0.02 * 0.02 } ) = 29° 44'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.02**2-0.01**2-0.02**2 }{ 2 * 0.01 * 0.02 } ) = 37° 38'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.02**2-0.01**2-0.02**2 }{ 2 * 0.02 * 0.01 } ) = 112° 37'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0 }{ 0.03 } = 0 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.01 }{ 2 * sin 29° 44'42" } = 0.01 ; ;





#2 Acute scalene triangle.

Sides: a = 0.013   b = 0.016   c = 0.01662788206

Area: T = 09.6E-5
Perimeter: p = 0.04552788206
Semiperimeter: s = 0.02326394103

Angle ∠ A = α = 47.4989552922° = 47°29'22″ = 0.82988490588 rad
Angle ∠ B = β = 65.1330312026° = 65°7'49″ = 1.13767383877 rad
Angle ∠ C = γ = 67.3880135052° = 67°22'49″ = 1.17660052071 rad

Height: ha = 0.01547692308
Height: hb = 0.012
Height: hc = 0.01217944662

Median: ma = 0.01547732867
Median: mb = 0.01223693169
Median: mc = 0.01220933866

Inradius: r = 0.00442403931
Circumradius: R = 0.00988176945

Vertex coordinates: A[0.01662788206; 0] B[0; 0] C[0.00554672265; 0.01217944662]
Centroid: CG[0.00772486824; 0.00439314887]
Coordinates of the circumscribed circle: U[0.00881394103; 0.0033391421]
Coordinates of the inscribed circle: I[0.00766394103; 0.00442403931]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.5110447078° = 132°30'38″ = 0.82988490588 rad
∠ B' = β' = 114.8769687974° = 114°52'11″ = 1.13767383877 rad
∠ C' = γ' = 112.6219864948° = 112°37'11″ = 1.17660052071 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 = 0.01 ; ; b = 0.02 ; ; c = 0.02 ; ; : Nr. 1

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

p = a+b+c = 0.01+0.02+0.02 = 0.05 ; ; : Nr. 1

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.05 }{ 2 } = 0.02 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.02 * (0.02-0.01)(0.02-0.02)(0.02-0.02) } ; ; T = sqrt{ 0 } = 0 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0 }{ 0.01 } = 0.01 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0 }{ 0.02 } = 0.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0 }{ 0.02 } = 0.01 ; ; : Nr. 1

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{ 0.01**2-0.02**2-0.02**2 }{ 2 * 0.02 * 0.02 } ) = 47° 29'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.02**2-0.01**2-0.02**2 }{ 2 * 0.01 * 0.02 } ) = 65° 7'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.02**2-0.01**2-0.02**2 }{ 2 * 0.02 * 0.01 } ) = 67° 22'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0 }{ 0.02 } = 0 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.01 }{ 2 * sin 47° 29'22" } = 0.01 ; ;




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