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 = 15   b = 36   c = 39

Area: T = 270
Perimeter: p = 90
Semiperimeter: s = 45

Angle ∠ A = α = 22.6219864948° = 22°37'11″ = 0.39547911197 rad
Angle ∠ B = β = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 36
Height: hb = 15
Height: hc = 13.84661538462

Median: ma = 36.77329520164
Median: mb = 23.43107490277
Median: mc = 19.5

Inradius: r = 6
Circumradius: R = 19.5

Vertex coordinates: A[39; 0] B[0; 0] C[5.76992307692; 13.84661538462]
Centroid: CG[14.92330769231; 4.61553846154]
Coordinates of the circumscribed circle: U[19.5; -0]
Coordinates of the inscribed circle: I[9; 6]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.3880135052° = 157°22'49″ = 0.39547911197 rad
∠ B' = β' = 112.6219864948° = 112°37'11″ = 1.17660052071 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 = 15 ; ; b = 36 ; ; c = 39 ; ;


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 = 15 ; ; b = 36 ; ; c = 39 ; ; : Nr. 1

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

p = a+b+c = 15+36+39 = 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 * (45-15)(45-36)(45-39) } ; ; T = sqrt{ 72900 } = 270 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 270 }{ 15 } = 36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 270 }{ 36 } = 15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 270 }{ 39 } = 13.85 ; ;

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{ 15**2-36**2-39**2 }{ 2 * 36 * 39 } ) = 22° 37'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 36**2-15**2-39**2 }{ 2 * 15 * 39 } ) = 67° 22'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 39**2-15**2-36**2 }{ 2 * 36 * 15 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 270 }{ 45 } = 6 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 22° 37'11" } = 19.5 ; ;




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