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

Calculate another triangle




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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 7**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 9° 29'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-7**2-25**2 }{ 2 * 7 * 25 } ) = 26° 34'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-7**2-19**2 }{ 2 * 19 * 7 } ) = 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 ; ;




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