16 29 30 triangle

Acute scalene triangle.

Sides: a = 16   b = 29   c = 30

Area: T = 226.7122235003
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 31.41112725322° = 31°24'41″ = 0.54882301279 rad
Angle ∠ B = β = 70.84549899264° = 70°50'42″ = 1.23664783328 rad
Angle ∠ C = γ = 77.74437375414° = 77°44'37″ = 1.35768841929 rad

Height: ha = 28.33990293754
Height: hb = 15.63553265519
Height: hc = 15.11441490002

Median: ma = 28.39989436423
Median: mb = 19.17768089108
Median: mc = 17.98661057486

Inradius: r = 6.04656596001
Circumradius: R = 15.3549855291

Vertex coordinates: A[30; 0] B[0; 0] C[5.25; 15.11441490002]
Centroid: CG[11.75; 5.03880496667]
Coordinates of the circumscribed circle: U[15; 3.25985360909]
Coordinates of the inscribed circle: I[8.5; 6.04656596001]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.5898727468° = 148°35'19″ = 0.54882301279 rad
∠ B' = β' = 109.1555010074° = 109°9'18″ = 1.23664783328 rad
∠ C' = γ' = 102.2566262459° = 102°15'23″ = 1.35768841929 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 = 16 ; ; b = 29 ; ; c = 30 ; ;

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

p = a+b+c = 16+29+30 = 75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75 }{ 2 } = 37.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.5 * (37.5-16)(37.5-29)(37.5-30) } ; ; T = sqrt{ 51398.44 } = 226.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 226.71 }{ 16 } = 28.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 226.71 }{ 29 } = 15.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 226.71 }{ 30 } = 15.11 ; ;

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{ 16**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 31° 24'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-16**2-30**2 }{ 2 * 16 * 30 } ) = 70° 50'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-16**2-29**2 }{ 2 * 29 * 16 } ) = 77° 44'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 226.71 }{ 37.5 } = 6.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 31° 24'41" } = 15.35 ; ;




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