7 10 13 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 10   c = 13

Area: T = 34.64110161514
Perimeter: p = 30
Semiperimeter: s = 15

Angle ∠ A = α = 32.2044227504° = 32°12'15″ = 0.5622069803 rad
Angle ∠ B = β = 49.58325617943° = 49°34'57″ = 0.86553789549 rad
Angle ∠ C = γ = 98.21332107017° = 98°12'48″ = 1.71441438957 rad

Height: ha = 9.89774331861
Height: hb = 6.92882032303
Height: hc = 5.32993871002

Median: ma = 11.05766721937
Median: mb = 9.16551513899
Median: mc = 5.67989083458

Inradius: r = 2.30994010768
Circumradius: R = 6.5677359312

Vertex coordinates: A[13; 0] B[0; 0] C[4.53884615385; 5.32993871002]
Centroid: CG[5.84661538462; 1.77664623667]
Coordinates of the circumscribed circle: U[6.5; -0.93881941874]
Coordinates of the inscribed circle: I[5; 2.30994010768]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.7965772496° = 147°47'45″ = 0.5622069803 rad
∠ B' = β' = 130.4177438206° = 130°25'3″ = 0.86553789549 rad
∠ C' = γ' = 81.78767892983° = 81°47'12″ = 1.71441438957 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 = 7 ; ; b = 10 ; ; c = 13 ; ;

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

p = a+b+c = 7+10+13 = 30 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 30 }{ 2 } = 15 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15 * (15-7)(15-10)(15-13) } ; ; T = sqrt{ 1200 } = 34.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.64 }{ 7 } = 9.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.64 }{ 10 } = 6.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.64 }{ 13 } = 5.33 ; ;

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{ 7**2-10**2-13**2 }{ 2 * 10 * 13 } ) = 32° 12'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-7**2-13**2 }{ 2 * 7 * 13 } ) = 49° 34'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-7**2-10**2 }{ 2 * 10 * 7 } ) = 98° 12'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.64 }{ 15 } = 2.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 32° 12'15" } = 6.57 ; ;




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