Triangle calculator

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

You have entered side a, b and c (hypotenuse-calculated).

Right scalene triangle.

Sides: a = 5.6   b = 9.6   c = 11.11439551916

Area: T = 26.88
Perimeter: p = 26.31439551916
Semiperimeter: s = 13.15769775958

Angle ∠ A = α = 30.25664371635° = 30°15'23″ = 0.52880744484 rad
Angle ∠ B = β = 59.74435628365° = 59°44'37″ = 1.04327218784 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 9.6
Height: hb = 5.6
Height: hc = 4.8377161845

Median: ma = 10
Median: mb = 7.37656355658
Median: mc = 5.55769775958

Inradius: r = 2.04330224042
Circumradius: R = 5.55769775958

Vertex coordinates: A[11.11439551916; 0] B[0; 0] C[2.82216777429; 4.8377161845]
Centroid: CG[4.64552109782; 1.61223872817]
Coordinates of the circumscribed circle: U[5.55769775958; -0]
Coordinates of the inscribed circle: I[3.55769775958; 2.04330224042]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.74435628365° = 149°44'37″ = 0.52880744484 rad
∠ B' = β' = 120.25664371635° = 120°15'23″ = 1.04327218784 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 (hypotenuse-calculated).

a = 5.6 ; ; b = 9.6 ; ; c = 11.114 ; ;


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 = 5.6 ; ; b = 9.6 ; ; c = 11.11 ; ;

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

p = a+b+c = 5.6+9.6+11.11 = 26.31 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26.31 }{ 2 } = 13.16 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.16 * (13.16-5.6)(13.16-9.6)(13.16-11.11) } ; ; T = sqrt{ 722.53 } = 26.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.88 }{ 5.6 } = 9.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.88 }{ 9.6 } = 5.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.88 }{ 11.11 } = 4.84 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 9.6**2+11.11**2-5.6**2 }{ 2 * 9.6 * 11.11 } ) = 30° 15'23" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5.6**2+11.11**2-9.6**2 }{ 2 * 5.6 * 11.11 } ) = 59° 44'37" ; ; gamma = 180° - alpha - beta = 180° - 30° 15'23" - 59° 44'37" = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.88 }{ 13.16 } = 2.04 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5.6 }{ 2 * sin 30° 15'23" } = 5.56 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.6**2+2 * 11.11**2 - 5.6**2 } }{ 2 } = 10 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.11**2+2 * 5.6**2 - 9.6**2 } }{ 2 } = 7.376 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.6**2+2 * 5.6**2 - 11.11**2 } }{ 2 } = 5.557 ; ;
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