11 15 25 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 15   c = 25

Area: T = 44.05989094282
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 13.59904939668° = 13°35'26″ = 0.23771988667 rad
Angle ∠ B = β = 18.68988366206° = 18°41'20″ = 0.32661817324 rad
Angle ∠ C = γ = 147.7210669413° = 147°43'14″ = 2.57882120545 rad

Height: ha = 8.01107108051
Height: hb = 5.87545212571
Height: hc = 3.52547127543

Median: ma = 19.86883164863
Median: mb = 17.79774717306
Median: mc = 4.09326763859

Inradius: r = 1.72878003697
Circumradius: R = 23.40661626442

Vertex coordinates: A[25; 0] B[0; 0] C[10.42; 3.52547127543]
Centroid: CG[11.80766666667; 1.17549042514]
Coordinates of the circumscribed circle: U[12.5; -19.78988465992]
Coordinates of the inscribed circle: I[10.5; 1.72878003697]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.4109506033° = 166°24'34″ = 0.23771988667 rad
∠ B' = β' = 161.3111163379° = 161°18'40″ = 0.32661817324 rad
∠ C' = γ' = 32.27993305874° = 32°16'46″ = 2.57882120545 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 = 11 ; ; b = 15 ; ; c = 25 ; ;

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

p = a+b+c = 11+15+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 * (25.5-11)(25.5-15)(25.5-25) } ; ; T = sqrt{ 1941.19 } = 44.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.06 }{ 11 } = 8.01 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.06 }{ 15 } = 5.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.06 }{ 25 } = 3.52 ; ;

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{ 11**2-15**2-25**2 }{ 2 * 15 * 25 } ) = 13° 35'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-11**2-25**2 }{ 2 * 11 * 25 } ) = 18° 41'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-11**2-15**2 }{ 2 * 15 * 11 } ) = 147° 43'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.06 }{ 25.5 } = 1.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 13° 35'26" } = 23.41 ; ;




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