13 25 26 triangle

Acute scalene triangle.

Sides: a = 13   b = 25   c = 26

Area: T = 159.8799874843
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 29.45218475231° = 29°27'7″ = 0.51440317101 rad
Angle ∠ B = β = 71.00875361503° = 71°27″ = 1.23993152996 rad
Angle ∠ C = γ = 79.54106163266° = 79°32'26″ = 1.3888245644 rad

Height: ha = 24.58545961298
Height: hb = 12.78439899875
Height: hc = 12.29222980649

Median: ma = 24.66327249103
Median: mb = 16.31771688721
Median: mc = 15.10996688705

Inradius: r = 4.99437460889
Circumradius: R = 13.22196599157

Vertex coordinates: A[26; 0] B[0; 0] C[4.23107692308; 12.29222980649]
Centroid: CG[10.07769230769; 4.09774326883]
Coordinates of the circumscribed circle: U[13; 2.43998767232]
Coordinates of the inscribed circle: I[7; 4.99437460889]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.5488152477° = 150°32'53″ = 0.51440317101 rad
∠ B' = β' = 108.992246385° = 108°59'33″ = 1.23993152996 rad
∠ C' = γ' = 100.4599383673° = 100°27'34″ = 1.3888245644 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 = 13 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 13+25+26 = 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 * (32-13)(32-25)(32-26) } ; ; T = sqrt{ 25536 } = 159.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 159.8 }{ 13 } = 24.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 159.8 }{ 25 } = 12.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 159.8 }{ 26 } = 12.29 ; ;

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{ 13**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 29° 27'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-13**2-26**2 }{ 2 * 13 * 26 } ) = 71° 27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-13**2-25**2 }{ 2 * 25 * 13 } ) = 79° 32'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 159.8 }{ 32 } = 4.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 29° 27'7" } = 13.22 ; ;




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