4 25 26 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 25   c = 26

Area: T = 49.22884216688
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 8.71222446146° = 8°42'44″ = 0.15220573538 rad
Angle ∠ B = β = 71.20990972776° = 71°12'33″ = 1.24328332049 rad
Angle ∠ C = γ = 100.0798658108° = 100°4'43″ = 1.7476702095 rad

Height: ha = 24.61442108344
Height: hb = 3.93882737335
Height: hc = 3.78768016668

Median: ma = 25.42663642702
Median: mb = 13.7754977314
Median: mc = 12.30985336251

Inradius: r = 1.79901244243
Circumradius: R = 13.20437546191

Vertex coordinates: A[26; 0] B[0; 0] C[1.28884615385; 3.78768016668]
Centroid: CG[9.09661538462; 1.26222672223]
Coordinates of the circumscribed circle: U[13; -2.31106570583]
Coordinates of the inscribed circle: I[2.5; 1.79901244243]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.2887755385° = 171°17'16″ = 0.15220573538 rad
∠ B' = β' = 108.7910902722° = 108°47'27″ = 1.24328332049 rad
∠ C' = γ' = 79.92113418922° = 79°55'17″ = 1.7476702095 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 = 4 ; ; b = 25 ; ; c = 26 ; ;

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

p = a+b+c = 4+25+26 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-4)(27.5-25)(27.5-26) } ; ; T = sqrt{ 2423.44 } = 49.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 49.23 }{ 4 } = 24.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 49.23 }{ 25 } = 3.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 49.23 }{ 26 } = 3.79 ; ;

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{ 4**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 8° 42'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-4**2-26**2 }{ 2 * 4 * 26 } ) = 71° 12'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-4**2-25**2 }{ 2 * 25 * 4 } ) = 100° 4'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 49.23 }{ 27.5 } = 1.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 8° 42'44" } = 13.2 ; ;




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