9 21 26 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 21   c = 26

Area: T = 86.30217960416
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 18.42986696038° = 18°25'43″ = 0.32216409613 rad
Angle ∠ B = β = 47.52992544904° = 47°31'45″ = 0.83295419819 rad
Angle ∠ C = γ = 114.0422075906° = 114°2'31″ = 1.99904097104 rad

Height: ha = 19.17881768981
Height: hb = 8.21992186706
Height: hc = 6.63985996955

Median: ma = 23.22002155162
Median: mb = 16.37883393542
Median: mc = 9.59216630466

Inradius: r = 3.08222070015
Circumradius: R = 14.23549297042

Vertex coordinates: A[26; 0] B[0; 0] C[6.07769230769; 6.63985996955]
Centroid: CG[10.69223076923; 2.21328665652]
Coordinates of the circumscribed circle: U[13; -5.79994158054]
Coordinates of the inscribed circle: I[7; 3.08222070015]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.5711330396° = 161°34'17″ = 0.32216409613 rad
∠ B' = β' = 132.471074551° = 132°28'15″ = 0.83295419819 rad
∠ C' = γ' = 65.95879240942° = 65°57'29″ = 1.99904097104 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 = 21 ; ; c = 26 ; ;

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

p = a+b+c = 9+21+26 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-9)(28-21)(28-26) } ; ; T = sqrt{ 7448 } = 86.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 86.3 }{ 9 } = 19.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 86.3 }{ 21 } = 8.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 86.3 }{ 26 } = 6.64 ; ;

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{ 21**2+26**2-9**2 }{ 2 * 21 * 26 } ) = 18° 25'43" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9**2+26**2-21**2 }{ 2 * 9 * 26 } ) = 47° 31'45" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 9**2+21**2-26**2 }{ 2 * 9 * 21 } ) = 114° 2'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 86.3 }{ 28 } = 3.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 18° 25'43" } = 14.23 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 21**2+2 * 26**2 - 9**2 } }{ 2 } = 23.2 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 9**2 - 21**2 } }{ 2 } = 16.378 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 21**2+2 * 9**2 - 26**2 } }{ 2 } = 9.592 ; ;
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