9 25 30 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 25   c = 30

Area: T = 101.5098620324
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 15.70553094058° = 15°42'19″ = 0.27441093592 rad
Angle ∠ B = β = 48.75765958652° = 48°45'24″ = 0.85109631299 rad
Angle ∠ C = γ = 115.5388094729° = 115°32'17″ = 2.01765201645 rad

Height: ha = 22.5577471183
Height: hb = 8.12106896259
Height: hc = 6.76772413549

Median: ma = 27.24442654517
Median: mb = 18.28325052988
Median: mc = 11.3143708499

Inradius: r = 3.17221443851
Circumradius: R = 16.62442038816

Vertex coordinates: A[30; 0] B[0; 0] C[5.93333333333; 6.76772413549]
Centroid: CG[11.97877777778; 2.25657471183]
Coordinates of the circumscribed circle: U[15; -7.16768790067]
Coordinates of the inscribed circle: I[7; 3.17221443851]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.2954690594° = 164°17'41″ = 0.27441093592 rad
∠ B' = β' = 131.2433404135° = 131°14'36″ = 0.85109631299 rad
∠ C' = γ' = 64.4621905271° = 64°27'43″ = 2.01765201645 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 = 9 ; ; b = 25 ; ; c = 30 ; ;

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

p = a+b+c = 9+25+30 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-9)(32-25)(32-30) } ; ; T = sqrt{ 10304 } = 101.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 101.51 }{ 9 } = 22.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 101.51 }{ 25 } = 8.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 101.51 }{ 30 } = 6.77 ; ;

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{ 9**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 15° 42'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-9**2-30**2 }{ 2 * 9 * 30 } ) = 48° 45'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-9**2-25**2 }{ 2 * 25 * 9 } ) = 115° 32'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 101.51 }{ 32 } = 3.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 15° 42'19" } = 16.62 ; ;




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