17 28 30 triangle

Acute scalene triangle.

Sides: a = 17   b = 28   c = 30

Area: T = 234.0377256649
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 33.86545572968° = 33°51'52″ = 0.59110480246 rad
Angle ∠ B = β = 66.60655603774° = 66°36'20″ = 1.16224863287 rad
Angle ∠ C = γ = 79.53298823258° = 79°31'48″ = 1.38880583003 rad

Height: ha = 27.53437948999
Height: hb = 16.71769469035
Height: hc = 15.60224837766

Median: ma = 27.7444368798
Median: mb = 19.96224647777
Median: mc = 17.64993625947

Inradius: r = 6.24109935107
Circumradius: R = 15.25439815716

Vertex coordinates: A[30; 0] B[0; 0] C[6.75; 15.60224837766]
Centroid: CG[12.25; 5.20108279255]
Coordinates of the circumscribed circle: U[15; 2.77219945503]
Coordinates of the inscribed circle: I[9.5; 6.24109935107]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.1355442703° = 146°8'8″ = 0.59110480246 rad
∠ B' = β' = 113.3944439623° = 113°23'40″ = 1.16224863287 rad
∠ C' = γ' = 100.4770117674° = 100°28'12″ = 1.38880583003 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 = 17 ; ; b = 28 ; ; c = 30 ; ;

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

p = a+b+c = 17+28+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 * (37.5-17)(37.5-28)(37.5-30) } ; ; T = sqrt{ 54773.44 } = 234.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 234.04 }{ 17 } = 27.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 234.04 }{ 28 } = 16.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 234.04 }{ 30 } = 15.6 ; ;

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{ 17**2-28**2-30**2 }{ 2 * 28 * 30 } ) = 33° 51'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 66° 36'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-28**2 }{ 2 * 28 * 17 } ) = 79° 31'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 234.04 }{ 37.5 } = 6.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 33° 51'52" } = 15.25 ; ;




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