Triangle calculator

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

You have entered side a, b and c.

Right scalene triangle.

Sides: a = 9   b = 40   c = 41

Area: T = 180
Perimeter: p = 90
Semiperimeter: s = 45

Angle ∠ A = α = 12.68803834918° = 12°40'49″ = 0.22113144423 rad
Angle ∠ B = β = 77.32196165082° = 77°19'11″ = 1.34994818844 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 40
Height: hb = 9
Height: hc = 8.78804878049

Median: ma = 40.25223291252
Median: mb = 21.93217121995
Median: mc = 20.5

Inradius: r = 4
Circumradius: R = 20.5

Vertex coordinates: A[41; 0] B[0; 0] C[1.97656097561; 8.78804878049]
Centroid: CG[14.3255203252; 2.92768292683]
Coordinates of the circumscribed circle: U[20.5; -0]
Coordinates of the inscribed circle: I[5; 4]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.3219616508° = 167°19'11″ = 0.22113144423 rad
∠ B' = β' = 102.6880383492° = 102°40'49″ = 1.34994818844 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 9 ; ; b = 40 ; ; c = 41 ; ;


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 = 9 ; ; b = 40 ; ; c = 41 ; ; : Nr. 1

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

p = a+b+c = 9+40+41 = 90 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 90 }{ 2 } = 45 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 45 * (45-9)(45-40)(45-41) } ; ; T = sqrt{ 32400 } = 180 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 180 }{ 9 } = 40 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 180 }{ 40 } = 9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 180 }{ 41 } = 8.78 ; ;

6. 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{ 9**2-40**2-41**2 }{ 2 * 40 * 41 } ) = 12° 40'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 40**2-9**2-41**2 }{ 2 * 9 * 41 } ) = 77° 19'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 41**2-9**2-40**2 }{ 2 * 40 * 9 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 180 }{ 45 } = 4 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 12° 40'49" } = 20.5 ; ;

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