79 97 63 triangle

Acute scalene triangle.

Sides: a = 79   b = 97   c = 63

Area: T = 2480.432983926
Perimeter: p = 239
Semiperimeter: s = 119.5

Angle ∠ A = α = 54.27113661771° = 54°16'17″ = 0.94772140293 rad
Angle ∠ B = β = 85.38444087918° = 85°23'4″ = 1.49902390633 rad
Angle ∠ C = γ = 40.34442250311° = 40°20'39″ = 0.7044139561 rad

Height: ha = 62.79656921332
Height: hb = 51.14328832837
Height: hc = 78.7443804421

Median: ma = 71.61552916632
Median: mb = 52.46766560779
Median: mc = 82.66604500351

Inradius: r = 20.75767350566
Circumradius: R = 48.65877963584

Vertex coordinates: A[63; 0] B[0; 0] C[6.35771428571; 78.7443804421]
Centroid: CG[23.1199047619; 26.2487934807]
Coordinates of the circumscribed circle: U[31.5; 37.08554573445]
Coordinates of the inscribed circle: I[22.5; 20.75767350566]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.7298633823° = 125°43'43″ = 0.94772140293 rad
∠ B' = β' = 94.61655912082° = 94°36'56″ = 1.49902390633 rad
∠ C' = γ' = 139.6565774969° = 139°39'21″ = 0.7044139561 rad

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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 = 79 ; ; b = 97 ; ; c = 63 ; ;

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

p = a+b+c = 79+97+63 = 239 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 239 }{ 2 } = 119.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 119.5 * (119.5-79)(119.5-97)(119.5-63) } ; ; T = sqrt{ 6152532.19 } = 2480.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2480.43 }{ 79 } = 62.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2480.43 }{ 97 } = 51.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2480.43 }{ 63 } = 78.74 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 97**2+63**2-79**2 }{ 2 * 97 * 63 } ) = 54° 16'17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 79**2+63**2-97**2 }{ 2 * 79 * 63 } ) = 85° 23'4" ; ; gamma = 180° - alpha - beta = 180° - 54° 16'17" - 85° 23'4" = 40° 20'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2480.43 }{ 119.5 } = 20.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 79 }{ 2 * sin 54° 16'17" } = 48.66 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 97**2+2 * 63**2 - 79**2 } }{ 2 } = 71.615 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 63**2+2 * 79**2 - 97**2 } }{ 2 } = 52.467 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 97**2+2 * 79**2 - 63**2 } }{ 2 } = 82.66 ; ;
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