15 23 25 triangle

Acute scalene triangle.

Sides: a = 15   b = 23   c = 25

Area: T = 169.45985126218
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 36.11659252263° = 36°6'57″ = 0.63303418076 rad
Angle ∠ B = β = 64.65992980761° = 64°39'33″ = 1.12985176435 rad
Angle ∠ C = γ = 79.22547766976° = 79°13'29″ = 1.38327332025 rad

Height: ha = 22.59444683496
Height: hb = 14.73655228367
Height: hc = 13.55766810097

Median: ma = 22.82199474145
Median: mb = 17.11099386323
Median: mc = 14.85876579581

Inradius: r = 5.38796353213
Circumradius: R = 12.72443533927

Vertex coordinates: A[25; 0] B[0; 0] C[6.42; 13.55766810097]
Centroid: CG[10.47333333333; 4.51988936699]
Coordinates of the circumscribed circle: U[12.5; 2.37989008517]
Coordinates of the inscribed circle: I[8.5; 5.38796353213]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.88440747737° = 143°53'3″ = 0.63303418076 rad
∠ B' = β' = 115.3410701924° = 115°20'27″ = 1.12985176435 rad
∠ C' = γ' = 100.77552233024° = 100°46'31″ = 1.38327332025 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 = 15 ; ; b = 23 ; ; c = 25 ; ;

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

p = a+b+c = 15+23+25 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-15)(31.5-23)(31.5-25) } ; ; T = sqrt{ 28716.19 } = 169.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 169.46 }{ 15 } = 22.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 169.46 }{ 23 } = 14.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 169.46 }{ 25 } = 13.56 ; ;

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{ 23**2+25**2-15**2 }{ 2 * 23 * 25 } ) = 36° 6'57" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15**2+25**2-23**2 }{ 2 * 15 * 25 } ) = 64° 39'33" ; ; gamma = 180° - alpha - beta = 180° - 36° 6'57" - 64° 39'33" = 79° 13'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 169.46 }{ 31.5 } = 5.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 36° 6'57" } = 12.72 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 25**2 - 15**2 } }{ 2 } = 22.82 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 15**2 - 23**2 } }{ 2 } = 17.11 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 15**2 - 25**2 } }{ 2 } = 14.858 ; ;
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