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

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 = 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" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; 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 = 180° - alpha - beta = 180° - 18° 25'43" - 47° 31'45" = 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 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.