7 25 26 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 25   c = 26

Area: T = 87.49985714169
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 15.61882367682° = 15°37'6″ = 0.2732589655 rad
Angle ∠ B = β = 74.05443569956° = 74°3'16″ = 1.2922492355 rad
Angle ∠ C = γ = 90.32774062362° = 90°19'39″ = 1.57765106436 rad

Height: ha = 254.9995918334
Height: hb = 76.9998857134
Height: hc = 6.73106593398

Median: ma = 25.26436101933
Median: mb = 14.36114066163
Median: mc = 12.96114813968

Inradius: r = 3.01771921178
Circumradius: R = 133.0002122501

Vertex coordinates: A[26; 0] B[0; 0] C[1.92330769231; 6.73106593398]
Centroid: CG[9.30876923077; 2.24435531133]
Coordinates of the circumscribed circle: U[13; -0.07442869271]
Coordinates of the inscribed circle: I[4; 3.01771921178]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.3821763232° = 164°22'54″ = 0.2732589655 rad
∠ B' = β' = 105.9465643004° = 105°56'44″ = 1.2922492355 rad
∠ C' = γ' = 89.67325937638° = 89°40'21″ = 1.57765106436 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 = 7 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 7+25+26 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-7)(29-25)(29-26) } ; ; T = sqrt{ 7656 } = 87.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 87.5 }{ 7 } = 25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 87.5 }{ 25 } = 7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 87.5 }{ 26 } = 6.73 ; ;

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{ 7**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 15° 37'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-7**2-26**2 }{ 2 * 7 * 26 } ) = 74° 3'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-7**2-25**2 }{ 2 * 25 * 7 } ) = 90° 19'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 87.5 }{ 29 } = 3.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 15° 37'6" } = 13 ; ;




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