7 29 30 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 29   c = 30

Area: T = 101.4699207152
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 13.48992278626° = 13°29'21″ = 0.23554314398 rad
Angle ∠ B = β = 75.09994033122° = 75°5'58″ = 1.31107318541 rad
Angle ∠ C = γ = 91.41113688253° = 91°24'41″ = 1.59554293598 rad

Height: ha = 28.99112020434
Height: hb = 6.99878763553
Height: hc = 6.76546138101

Median: ma = 29.29659041506
Median: mb = 16.2565768207
Median: mc = 14.83223969742

Inradius: r = 3.07548244591
Circumradius: R = 15.00545520482

Vertex coordinates: A[30; 0] B[0; 0] C[1.8; 6.76546138101]
Centroid: CG[10.6; 2.255487127]
Coordinates of the circumscribed circle: U[15; -0.37695702475]
Coordinates of the inscribed circle: I[4; 3.07548244591]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.5110772137° = 166°30'39″ = 0.23554314398 rad
∠ B' = β' = 104.9010596688° = 104°54'2″ = 1.31107318541 rad
∠ C' = γ' = 88.58986311747° = 88°35'19″ = 1.59554293598 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 = 29 ; ; c = 30 ; ;

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

p = a+b+c = 7+29+30 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-7)(33-29)(33-30) } ; ; T = sqrt{ 10296 } = 101.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 101.47 }{ 7 } = 28.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 101.47 }{ 29 } = 7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 101.47 }{ 30 } = 6.76 ; ;

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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 13° 29'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-7**2-30**2 }{ 2 * 7 * 30 } ) = 75° 5'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-7**2-29**2 }{ 2 * 29 * 7 } ) = 91° 24'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 101.47 }{ 33 } = 3.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 13° 29'21" } = 15 ; ;




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