98 85 29.82 triangle

Obtuse scalene triangle.

Sides: a = 98   b = 85   c = 29.82

Area: T = 1211.389889446
Perimeter: p = 212.82
Semiperimeter: s = 106.41

Angle ∠ A = α = 107.0990062218° = 107°5'24″ = 1.86990741819 rad
Angle ∠ B = β = 56.00111061415° = 56°4″ = 0.97774036869 rad
Angle ∠ C = γ = 16.90988316403° = 16°54'32″ = 0.29551147848 rad

Height: ha = 24.72222223359
Height: hb = 28.5033268105
Height: hc = 81.24767400712

Median: ma = 40.69554076033
Median: mb = 58.65546349405
Median: mc = 90.51107280934

Inradius: r = 11.38441640303
Circumradius: R = 51.26435952698

Vertex coordinates: A[29.82; 0] B[0; 0] C[54.79993360161; 81.24767400712]
Centroid: CG[28.20664453387; 27.08222466904]
Coordinates of the circumscribed circle: U[14.91; 49.04774066591]
Coordinates of the inscribed circle: I[21.41; 11.38441640303]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 72.91099377819° = 72°54'36″ = 1.86990741819 rad
∠ B' = β' = 123.9998893858° = 123°59'56″ = 0.97774036869 rad
∠ C' = γ' = 163.091116836° = 163°5'28″ = 0.29551147848 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 = 98 ; ; b = 85 ; ; c = 29.82 ; ;

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

p = a+b+c = 98+85+29.82 = 212.82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 212.82 }{ 2 } = 106.41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 106.41 * (106.41-98)(106.41-85)(106.41-29.82) } ; ; T = sqrt{ 1467463.05 } = 1211.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1211.39 }{ 98 } = 24.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1211.39 }{ 85 } = 28.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1211.39 }{ 29.82 } = 81.25 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 85**2+29.82**2-98**2 }{ 2 * 85 * 29.82 } ) = 107° 5'24" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 98**2+29.82**2-85**2 }{ 2 * 98 * 29.82 } ) = 56° 4" ; ;
 gamma = 180° - alpha - beta = 180° - 107° 5'24" - 56° 4" = 16° 54'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1211.39 }{ 106.41 } = 11.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 98 }{ 2 * sin 107° 5'24" } = 51.26 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 85**2+2 * 29.82**2 - 98**2 } }{ 2 } = 40.695 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29.82**2+2 * 98**2 - 85**2 } }{ 2 } = 58.655 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 85**2+2 * 98**2 - 29.82**2 } }{ 2 } = 90.511 ; ;
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