18.7 27.33 16.1 triangle

Obtuse scalene triangle.

Sides: a = 18.7   b = 27.33   c = 16.1

Area: T = 146.5276576592
Perimeter: p = 62.13
Semiperimeter: s = 31.065

Angle ∠ A = α = 41.76598731554° = 41°45'36″ = 0.72988472818 rad
Angle ∠ B = β = 103.2521776878° = 103°15'6″ = 1.80220834651 rad
Angle ∠ C = γ = 34.98883499669° = 34°59'18″ = 0.61106619068 rad

Height: ha = 15.67112916141
Height: hb = 10.7232764478
Height: hc = 18.2022059204

Median: ma = 20.38774213671
Median: mb = 10.85497822559
Median: mc = 21.98987914629

Inradius: r = 4.71767737516
Circumradius: R = 14.03988236922

Vertex coordinates: A[16.1; 0] B[0; 0] C[-4.28766118012; 18.2022059204]
Centroid: CG[3.93877960663; 6.0677353068]
Coordinates of the circumscribed circle: U[8.05; 11.50215681827]
Coordinates of the inscribed circle: I[3.735; 4.71767737516]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.2440126845° = 138°14'24″ = 0.72988472818 rad
∠ B' = β' = 76.74882231223° = 76°44'54″ = 1.80220834651 rad
∠ C' = γ' = 145.0121650033° = 145°42″ = 0.61106619068 rad

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How did we calculate this triangle?

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

p = a+b+c = 18.7+27.33+16.1 = 62.13 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62.13 }{ 2 } = 31.07 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.07 * (31.07-18.7)(31.07-27.33)(31.07-16.1) } ; ; T = sqrt{ 21470.04 } = 146.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 146.53 }{ 18.7 } = 15.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 146.53 }{ 27.33 } = 10.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 146.53 }{ 16.1 } = 18.2 ; ;

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{ 27.33**2+16.1**2-18.7**2 }{ 2 * 27.33 * 16.1 } ) = 41° 45'36" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18.7**2+16.1**2-27.33**2 }{ 2 * 18.7 * 16.1 } ) = 103° 15'6" ; ;
 gamma = 180° - alpha - beta = 180° - 41° 45'36" - 103° 15'6" = 34° 59'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 146.53 }{ 31.07 } = 4.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18.7 }{ 2 * sin 41° 45'36" } = 14.04 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 27.33**2+2 * 16.1**2 - 18.7**2 } }{ 2 } = 20.387 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 16.1**2+2 * 18.7**2 - 27.33**2 } }{ 2 } = 10.85 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 27.33**2+2 * 18.7**2 - 16.1**2 } }{ 2 } = 21.989 ; ;
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