7 19 25 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 19   c = 25

Area: T = 39.1565938247
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 9.49895146153° = 9°29'22″ = 0.16656232745 rad
Angle ∠ B = β = 26.58331710556° = 26°34'59″ = 0.46439638605 rad
Angle ∠ C = γ = 143.9277314329° = 143°55'38″ = 2.51220055186 rad

Height: ha = 11.18774109277
Height: hb = 4.12216777102
Height: hc = 3.13224750598

Median: ma = 21.92660119493
Median: mb = 15.70882780724
Median: mc = 6.98221200219

Inradius: r = 1.53655269901
Circumradius: R = 21.22992193015

Vertex coordinates: A[25; 0] B[0; 0] C[6.26; 3.13224750598]
Centroid: CG[10.42; 1.04441583533]
Coordinates of the circumscribed circle: U[12.5; -17.15989554504]
Coordinates of the inscribed circle: I[6.5; 1.53655269901]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.5110485385° = 170°30'38″ = 0.16656232745 rad
∠ B' = β' = 153.4176828944° = 153°25'1″ = 0.46439638605 rad
∠ C' = γ' = 36.07326856709° = 36°4'22″ = 2.51220055186 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 = 7 ; ; b = 19 ; ; c = 25 ; ;

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

p = a+b+c = 7+19+25 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-7)(25.5-19)(25.5-25) } ; ; T = sqrt{ 1533.19 } = 39.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.16 }{ 7 } = 11.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.16 }{ 19 } = 4.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.16 }{ 25 } = 3.13 ; ;

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{ 19**2+25**2-7**2 }{ 2 * 19 * 25 } ) = 9° 29'22" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+25**2-19**2 }{ 2 * 7 * 25 } ) = 26° 34'59" ; ; gamma = 180° - alpha - beta = 180° - 9° 29'22" - 26° 34'59" = 143° 55'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.16 }{ 25.5 } = 1.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7 }{ 2 * sin 9° 29'22" } = 21.23 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 25**2 - 7**2 } }{ 2 } = 21.926 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 7**2 - 19**2 } }{ 2 } = 15.708 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 7**2 - 25**2 } }{ 2 } = 6.982 ; ;
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