2 10 11 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 10   c = 11

Area: T = 9.05219334951
Perimeter: p = 23
Semiperimeter: s = 11.5

Angle ∠ A = α = 9.47328720666° = 9°28'22″ = 0.16553328072 rad
Angle ∠ B = β = 55.37664645208° = 55°22'35″ = 0.9676501634 rad
Angle ∠ C = γ = 115.1510663413° = 115°9'2″ = 2.01097582124 rad

Height: ha = 9.05219334951
Height: hb = 1.8110386699
Height: hc = 1.646580609

Median: ma = 10.46442247682
Median: mb = 6.1243724357
Median: mc = 4.66436895265

Inradius: r = 0.78771246517
Circumradius: R = 6.07660499433

Vertex coordinates: A[11; 0] B[0; 0] C[1.13663636364; 1.646580609]
Centroid: CG[4.04554545455; 0.549860203]
Coordinates of the circumscribed circle: U[5.5; -2.58223212259]
Coordinates of the inscribed circle: I[1.5; 0.78771246517]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.5277127933° = 170°31'38″ = 0.16553328072 rad
∠ B' = β' = 124.6243535479° = 124°37'25″ = 0.9676501634 rad
∠ C' = γ' = 64.84993365875° = 64°50'58″ = 2.01097582124 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 = 2 ; ; b = 10 ; ; c = 11 ; ;

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

p = a+b+c = 2+10+11 = 23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23 }{ 2 } = 11.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.5 * (11.5-2)(11.5-10)(11.5-11) } ; ; T = sqrt{ 81.94 } = 9.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9.05 }{ 2 } = 9.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9.05 }{ 10 } = 1.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9.05 }{ 11 } = 1.65 ; ;

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{ 2**2-10**2-11**2 }{ 2 * 10 * 11 } ) = 9° 28'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-2**2-11**2 }{ 2 * 2 * 11 } ) = 55° 22'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-2**2-10**2 }{ 2 * 10 * 2 } ) = 115° 9'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9.05 }{ 11.5 } = 0.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 9° 28'22" } = 6.08 ; ;




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