7 21 25 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 21   c = 25

Area: T = 65.29330892208
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 14.40327028211° = 14°24'10″ = 0.25113745854 rad
Angle ∠ B = β = 48.26328531992° = 48°15'46″ = 0.84223456947 rad
Angle ∠ C = γ = 117.334444398° = 117°20'4″ = 2.04878723734 rad

Height: ha = 18.65551683488
Height: hb = 6.21883894496
Height: hc = 5.22334471377

Median: ma = 22.82199474145
Median: mb = 15.05882203464
Median: mc = 9.42107218407

Inradius: r = 2.46438901593
Circumradius: R = 14.07111675763

Vertex coordinates: A[25; 0] B[0; 0] C[4.66; 5.22334471377]
Centroid: CG[9.88766666667; 1.74111490459]
Coordinates of the circumscribed circle: U[12.5; -6.46112504177]
Coordinates of the inscribed circle: I[5.5; 2.46438901593]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.5977297179° = 165°35'50″ = 0.25113745854 rad
∠ B' = β' = 131.7377146801° = 131°44'14″ = 0.84223456947 rad
∠ C' = γ' = 62.66655560203° = 62°39'56″ = 2.04878723734 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 = 21 ; ; c = 25 ; ;

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

p = a+b+c = 7+21+25 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-7)(26.5-21)(26.5-25) } ; ; T = sqrt{ 4263.19 } = 65.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 65.29 }{ 7 } = 18.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 65.29 }{ 21 } = 6.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 65.29 }{ 25 } = 5.22 ; ;

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**2-21**2-25**2 }{ 2 * 21 * 25 } ) = 14° 24'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-7**2-25**2 }{ 2 * 7 * 25 } ) = 48° 15'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-7**2-21**2 }{ 2 * 21 * 7 } ) = 117° 20'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 65.29 }{ 26.5 } = 2.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 14° 24'10" } = 14.07 ; ;




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