Triangle calculator - result

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 55   b = 36   c = 28

Area: T = 445.1998761791
Perimeter: p = 119
Semiperimeter: s = 59.5

Angle ∠ A = α = 117.9533186883° = 117°57'11″ = 2.05986714743 rad
Angle ∠ B = β = 35.32326498434° = 35°19'22″ = 0.61664965403 rad
Angle ∠ C = γ = 26.72441632732° = 26°43'27″ = 0.4666424639 rad

Height: ha = 16.18990458833
Height: hb = 24.73332645439
Height: hc = 31.87999115565

Median: ma = 16.84548805279
Median: mb = 39.75655027638
Median: mc = 44.32326804244

Inradius: r = 7.48223321309
Circumradius: R = 31.13221620578

Vertex coordinates: A[28; 0] B[0; 0] C[44.875; 31.87999115565]
Centroid: CG[24.29216666667; 10.65999705188]
Coordinates of the circumscribed circle: U[14; 27.80766811107]
Coordinates of the inscribed circle: I[23.5; 7.48223321309]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 62.04768131166° = 62°2'49″ = 2.05986714743 rad
∠ B' = β' = 144.6777350157° = 144°40'38″ = 0.61664965403 rad
∠ C' = γ' = 153.2765836727° = 153°16'33″ = 0.4666424639 rad

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How did we calculate this triangle?

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

a = 55 ; ; b = 36 ; ; c = 28 ; ;

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

p = a+b+c = 55+36+28 = 119 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 119 }{ 2 } = 59.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 59.5 * (59.5-55)(59.5-36)(59.5-28) } ; ; T = sqrt{ 198201.94 } = 445.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 445.2 }{ 55 } = 16.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 445.2 }{ 36 } = 24.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 445.2 }{ 28 } = 31.8 ; ;

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{ 36**2+28**2-55**2 }{ 2 * 36 * 28 } ) = 117° 57'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 55**2+28**2-36**2 }{ 2 * 55 * 28 } ) = 35° 19'22" ; ; gamma = 180° - alpha - beta = 180° - 117° 57'11" - 35° 19'22" = 26° 43'27" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 445.2 }{ 59.5 } = 7.48 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 55 }{ 2 * sin 117° 57'11" } = 31.13 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 36**2+2 * 28**2 - 55**2 } }{ 2 } = 16.845 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 55**2 - 36**2 } }{ 2 } = 39.756 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 36**2+2 * 55**2 - 28**2 } }{ 2 } = 44.323 ; ;
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