17 20 28 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 20   c = 28

Area: T = 168.3332817656
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 36.95550748363° = 36°57'18″ = 0.64549877312 rad
Angle ∠ B = β = 45.01440978737° = 45°51″ = 0.78656442177 rad
Angle ∠ C = γ = 98.03108272899° = 98°1'51″ = 1.71109607047 rad

Height: ha = 19.80438609007
Height: hb = 16.83332817656
Height: hc = 12.02437726897

Median: ma = 22.79880262304
Median: mb = 20.89325824158
Median: mc = 12.1866057607

Inradius: r = 5.17994713125
Circumradius: R = 14.13986571742

Vertex coordinates: A[28; 0] B[0; 0] C[12.01878571429; 12.02437726897]
Centroid: CG[13.33992857143; 4.00879242299]
Coordinates of the circumscribed circle: U[14; -1.97552535758]
Coordinates of the inscribed circle: I[12.5; 5.17994713125]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.0454925164° = 143°2'42″ = 0.64549877312 rad
∠ B' = β' = 134.9865902126° = 134°59'9″ = 0.78656442177 rad
∠ C' = γ' = 81.96991727101° = 81°58'9″ = 1.71109607047 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 = 20 ; ; c = 28 ; ;

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

p = a+b+c = 17+20+28 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-17)(32.5-20)(32.5-28) } ; ; T = sqrt{ 28335.94 } = 168.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 168.33 }{ 17 } = 19.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 168.33 }{ 20 } = 16.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 168.33 }{ 28 } = 12.02 ; ;

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**2-20**2-28**2 }{ 2 * 20 * 28 } ) = 36° 57'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 45° 51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-17**2-20**2 }{ 2 * 20 * 17 } ) = 98° 1'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 168.33 }{ 32.5 } = 5.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 36° 57'18" } = 14.14 ; ;




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