16 28 30 triangle

Acute scalene triangle.

Sides: a = 16   b = 28   c = 30

Area: T = 221.249872881
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 31.78883306171° = 31°47'18″ = 0.5554811033 rad
Angle ∠ B = β = 67.20109687281° = 67°12'3″ = 1.17328781648 rad
Angle ∠ C = γ = 81.01107006548° = 81°39″ = 1.41439034558 rad

Height: ha = 27.65660911012
Height: hb = 15.80334806293
Height: hc = 14.7549915254

Median: ma = 27.8932651362
Median: mb = 19.54548202857
Median: mc = 17.17655640373

Inradius: r = 5.98796953732
Circumradius: R = 15.1876527932

Vertex coordinates: A[30; 0] B[0; 0] C[6.2; 14.7549915254]
Centroid: CG[12.06766666667; 4.9176638418]
Coordinates of the circumscribed circle: U[15; 2.37328949894]
Coordinates of the inscribed circle: I[9; 5.98796953732]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.2121669383° = 148°12'42″ = 0.5554811033 rad
∠ B' = β' = 112.7999031272° = 112°47'57″ = 1.17328781648 rad
∠ C' = γ' = 98.98992993452° = 98°59'21″ = 1.41439034558 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 = 28 ; ; c = 30 ; ;

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

p = a+b+c = 16+28+30 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-16)(37-28)(37-30) } ; ; T = sqrt{ 48951 } = 221.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 221.25 }{ 16 } = 27.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 221.25 }{ 28 } = 15.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 221.25 }{ 30 } = 14.75 ; ;

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**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 31° 47'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-16**2-30**2 }{ 2 * 16 * 30 } ) = 67° 12'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-16**2-28**2 }{ 2 * 28 * 16 } ) = 81° 39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 221.25 }{ 37 } = 5.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 31° 47'18" } = 15.19 ; ;




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