38 31 35 triangle

Acute scalene triangle.

Sides: a = 38   b = 31   c = 35

Area: T = 509.8799960769
Perimeter: p = 104
Semiperimeter: s = 52

Angle ∠ A = α = 70.00551618474° = 70°19″ = 1.22218205676 rad
Angle ∠ B = β = 50.05110165987° = 50°3'4″ = 0.87435550336 rad
Angle ∠ C = γ = 59.94438215539° = 59°56'38″ = 1.04662170523 rad

Height: ha = 26.83215768826
Height: hb = 32.89903200496
Height: hc = 29.13114263297

Median: ma = 27.05554985169
Median: mb = 33.0799449814
Median: mc = 29.93774347598

Inradius: r = 9.80438453994
Circumradius: R = 20.21987147768

Vertex coordinates: A[35; 0] B[0; 0] C[24.4; 29.13114263297]
Centroid: CG[19.8; 9.71104754432]
Coordinates of the circumscribed circle: U[17.5; 10.12765209833]
Coordinates of the inscribed circle: I[21; 9.80438453994]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 109.9954838153° = 109°59'41″ = 1.22218205676 rad
∠ B' = β' = 129.9498983401° = 129°56'56″ = 0.87435550336 rad
∠ C' = γ' = 120.0566178446° = 120°3'22″ = 1.04662170523 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 = 38 ; ; b = 31 ; ; c = 35 ; ;

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

p = a+b+c = 38+31+35 = 104 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 104 }{ 2 } = 52 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 52 * (52-38)(52-31)(52-35) } ; ; T = sqrt{ 259896 } = 509.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 509.8 }{ 38 } = 26.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 509.8 }{ 31 } = 32.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 509.8 }{ 35 } = 29.13 ; ;

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{ 31**2+35**2-38**2 }{ 2 * 31 * 35 } ) = 70° 19" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 38**2+35**2-31**2 }{ 2 * 38 * 35 } ) = 50° 3'4" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 38**2+31**2-35**2 }{ 2 * 38 * 31 } ) = 59° 56'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 509.8 }{ 52 } = 9.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 38 }{ 2 * sin 70° 19" } = 20.22 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 31**2+2 * 35**2 - 38**2 } }{ 2 } = 27.055 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 35**2+2 * 38**2 - 31**2 } }{ 2 } = 33.079 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 31**2+2 * 38**2 - 35**2 } }{ 2 } = 29.937 ; ;
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