17 23 28 triangle

Acute scalene triangle.

Sides: a = 17   b = 23   c = 28

Area: T = 195.3155129982
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 37.3421810948° = 37°20'31″ = 0.65217375497 rad
Angle ∠ B = β = 55.1550095421° = 55°9' = 0.96325507479 rad
Angle ∠ C = γ = 87.5088093631° = 87°30'29″ = 1.5277304356 rad

Height: ha = 22.97882505862
Height: hb = 16.98439243463
Height: hc = 13.9511080713

Median: ma = 24.17112639305
Median: mb = 20.10659692629
Median: mc = 14.59545195193

Inradius: r = 5.74545626465
Circumradius: R = 14.01332513044

Vertex coordinates: A[28; 0] B[0; 0] C[9.71442857143; 13.9511080713]
Centroid: CG[12.57114285714; 4.65503602377]
Coordinates of the circumscribed circle: U[14; 0.60992717958]
Coordinates of the inscribed circle: I[11; 5.74545626465]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.6588189052° = 142°39'29″ = 0.65217375497 rad
∠ B' = β' = 124.8549904579° = 124°51' = 0.96325507479 rad
∠ C' = γ' = 92.4921906369° = 92°29'31″ = 1.5277304356 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 = 23 ; ; c = 28 ; ;

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

p = a+b+c = 17+23+28 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-17)(34-23)(34-28) } ; ; T = sqrt{ 38148 } = 195.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 195.32 }{ 17 } = 22.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 195.32 }{ 23 } = 16.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 195.32 }{ 28 } = 13.95 ; ;

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**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 37° 20'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 55° 9' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-17**2-23**2 }{ 2 * 23 * 17 } ) = 87° 30'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 195.32 }{ 34 } = 5.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 37° 20'31" } = 14.01 ; ;




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