5 21 25 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 21   c = 25

Area: T = 34.29655900955
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 7.50771472486° = 7°30'26″ = 0.13110244369 rad
Angle ∠ B = β = 33.28798909447° = 33°16'48″ = 0.58108436717 rad
Angle ∠ C = γ = 139.2132961807° = 139°12'47″ = 2.4329724545 rad

Height: ha = 13.71882360382
Height: hb = 3.26662466758
Height: hc = 2.74436472076

Median: ma = 22.95110348351
Median: mb = 14.65443508898
Median: mc = 8.7610707734

Inradius: r = 1.34549251018
Circumradius: R = 19.13551132368

Vertex coordinates: A[25; 0] B[0; 0] C[4.18; 2.74436472076]
Centroid: CG[9.72766666667; 0.91545490692]
Coordinates of the circumscribed circle: U[12.5; -14.48880143078]
Coordinates of the inscribed circle: I[4.5; 1.34549251018]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.4932852751° = 172°29'34″ = 0.13110244369 rad
∠ B' = β' = 146.7220109055° = 146°43'12″ = 0.58108436717 rad
∠ C' = γ' = 40.78770381933° = 40°47'13″ = 2.4329724545 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 = 5 ; ; b = 21 ; ; c = 25 ; ;

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

p = a+b+c = 5+21+25 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-5)(25.5-21)(25.5-25) } ; ; T = sqrt{ 1176.19 } = 34.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.3 }{ 5 } = 13.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.3 }{ 21 } = 3.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.3 }{ 25 } = 2.74 ; ;

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{ 5**2-21**2-25**2 }{ 2 * 21 * 25 } ) = 7° 30'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-5**2-25**2 }{ 2 * 5 * 25 } ) = 33° 16'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-5**2-21**2 }{ 2 * 21 * 5 } ) = 139° 12'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.3 }{ 25.5 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 7° 30'26" } = 19.14 ; ;




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