52.15 48 60 triangle

Acute scalene triangle.

Sides: a = 52.15   b = 48   c = 60

Area: T = 1199.931072554
Perimeter: p = 160.15
Semiperimeter: s = 80.075

Angle ∠ A = α = 56.43877041527° = 56°26'16″ = 0.98550237597 rad
Angle ∠ B = β = 50.08329233523° = 50°4'59″ = 0.87441119115 rad
Angle ∠ C = γ = 73.47993724951° = 73°28'46″ = 1.28224569823 rad

Height: ha = 46.01884362623
Height: hb = 49.99771135641
Height: hc = 39.99876908513

Median: ma = 47.66664911127
Median: mb = 50.83112035073
Median: mc = 40.14773691542

Inradius: r = 14.98550855515
Circumradius: R = 31.29218064358

Vertex coordinates: A[60; 0] B[0; 0] C[33.46435208333; 39.99876908513]
Centroid: CG[31.15545069444; 13.33325636171]
Coordinates of the circumscribed circle: U[30; 8.8988154304]
Coordinates of the inscribed circle: I[32.075; 14.98550855515]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.5622295847° = 123°33'44″ = 0.98550237597 rad
∠ B' = β' = 129.9177076648° = 129°55'1″ = 0.87441119115 rad
∠ C' = γ' = 106.5210627505° = 106°31'14″ = 1.28224569823 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 = 52.15 ; ; b = 48 ; ; c = 60 ; ;

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

p = a+b+c = 52.15+48+60 = 160.15 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 160.15 }{ 2 } = 80.08 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 80.08 * (80.08-52.15)(80.08-48)(80.08-60) } ; ; T = sqrt{ 1439833.75 } = 1199.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1199.93 }{ 52.15 } = 46.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1199.93 }{ 48 } = 50 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1199.93 }{ 60 } = 40 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 48**2+60**2-52.15**2 }{ 2 * 48 * 60 } ) = 56° 26'16" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 52.15**2+60**2-48**2 }{ 2 * 52.15 * 60 } ) = 50° 4'59" ; ; gamma = 180° - alpha - beta = 180° - 56° 26'16" - 50° 4'59" = 73° 28'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1199.93 }{ 80.08 } = 14.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 52.15 }{ 2 * sin 56° 26'16" } = 31.29 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 48**2+2 * 60**2 - 52.15**2 } }{ 2 } = 47.666 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 52.15**2 - 48**2 } }{ 2 } = 50.831 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 48**2+2 * 52.15**2 - 60**2 } }{ 2 } = 40.147 ; ;
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