300 77.65 289.78 triangle

Acute scalene triangle.

Sides: a = 300   b = 77.65   c = 289.78

Area: T = 11250.70884892
Perimeter: p = 667.43
Semiperimeter: s = 333.715

Angle ∠ A = α = 89.99774907302° = 89°59'51″ = 1.57107525318 rad
Angle ∠ B = β = 15.00108475213° = 15°3″ = 0.26218141798 rad
Angle ∠ C = γ = 75.00216617485° = 75°6″ = 1.3099025942 rad

Height: ha = 75.00547232614
Height: hb = 289.7879999722
Height: hc = 77.65499999255

Median: ma = 150.0033284797
Median: mb = 292.3687651383
Median: mc = 164.3832630317

Inradius: r = 33.71435234832
Circumradius: R = 1500.000000144

Vertex coordinates: A[289.78; 0] B[0; 0] C[289.7776599317; 77.65499999255]
Centroid: CG[193.1865533106; 25.88333333085]
Coordinates of the circumscribed circle: U[144.89; 38.81986545768]
Coordinates of the inscribed circle: I[256.065; 33.71435234832]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.00325092698° = 90°9″ = 1.57107525318 rad
∠ B' = β' = 164.9999152479° = 164°59'57″ = 0.26218141798 rad
∠ C' = γ' = 104.9988338252° = 104°59'54″ = 1.3099025942 rad

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How did we calculate this triangle?

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

p = a+b+c = 300+77.65+289.78 = 667.43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 667.43 }{ 2 } = 333.72 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 333.72 * (333.72-300)(333.72-77.65)(333.72-289.78) } ; ; T = sqrt{ 126578441.51 } = 11250.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11250.71 }{ 300 } = 75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11250.71 }{ 77.65 } = 289.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11250.71 }{ 289.78 } = 77.65 ; ;

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{ 77.65**2+289.78**2-300**2 }{ 2 * 77.65 * 289.78 } ) = 89° 59'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 300**2+289.78**2-77.65**2 }{ 2 * 300 * 289.78 } ) = 15° 3" ; ;
 gamma = 180° - alpha - beta = 180° - 89° 59'51" - 15° 3" = 75° 6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11250.71 }{ 333.72 } = 33.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 300 }{ 2 * sin 89° 59'51" } = 150 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 77.65**2+2 * 289.78**2 - 300**2 } }{ 2 } = 150.003 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 289.78**2+2 * 300**2 - 77.65**2 } }{ 2 } = 292.368 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 77.65**2+2 * 300**2 - 289.78**2 } }{ 2 } = 164.383 ; ;
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