10 25 30 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 25   c = 30

Area: T = 117.094371247
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 18.19548723388° = 18°11'42″ = 0.31875604293 rad
Angle ∠ B = β = 51.31878125465° = 51°19'4″ = 0.89656647939 rad
Angle ∠ C = γ = 110.4877315115° = 110°29'14″ = 1.92883674304 rad

Height: ha = 23.4198742494
Height: hb = 9.36774969976
Height: hc = 7.8066247498

Median: ma = 27.1576951228
Median: mb = 18.54404962177
Median: mc = 11.72660393996

Inradius: r = 3.60328834606
Circumradius: R = 16.01328153805

Vertex coordinates: A[30; 0] B[0; 0] C[6.25; 7.8066247498]
Centroid: CG[12.08333333333; 2.60220824993]
Coordinates of the circumscribed circle: U[15; -5.60444853832]
Coordinates of the inscribed circle: I[7.5; 3.60328834606]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.8055127661° = 161°48'18″ = 0.31875604293 rad
∠ B' = β' = 128.6822187453° = 128°40'56″ = 0.89656647939 rad
∠ C' = γ' = 69.51326848853° = 69°30'46″ = 1.92883674304 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 = 10 ; ; b = 25 ; ; c = 30 ; ;

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

p = a+b+c = 10+25+30 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-10)(32.5-25)(32.5-30) } ; ; T = sqrt{ 13710.94 } = 117.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 117.09 }{ 10 } = 23.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 117.09 }{ 25 } = 9.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 117.09 }{ 30 } = 7.81 ; ;

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{ 25**2+30**2-10**2 }{ 2 * 25 * 30 } ) = 18° 11'42" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+30**2-25**2 }{ 2 * 10 * 30 } ) = 51° 19'4" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 10**2+25**2-30**2 }{ 2 * 10 * 25 } ) = 110° 29'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 117.09 }{ 32.5 } = 3.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 18° 11'42" } = 16.01 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 30**2 - 10**2 } }{ 2 } = 27.157 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 10**2 - 25**2 } }{ 2 } = 18.54 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 10**2 - 30**2 } }{ 2 } = 11.726 ; ;
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