2 9 10 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 9   c = 10

Area: T = 8.1821534086
Perimeter: p = 21
Semiperimeter: s = 10.5

Angle ∠ A = α = 10.47553138432° = 10°28'31″ = 0.18328287167 rad
Angle ∠ B = β = 54.99003678046° = 54°54'1″ = 0.95881921787 rad
Angle ∠ C = γ = 114.6244318352° = 114°37'28″ = 2.00105717581 rad

Height: ha = 8.1821534086
Height: hb = 1.81881186858
Height: hc = 1.63663068172

Median: ma = 9.46604439642
Median: mb = 5.63547138348
Median: mc = 4.18333001327

Inradius: r = 0.77991937225
Circumradius: R = 5.55001909822

Vertex coordinates: A[10; 0] B[0; 0] C[1.15; 1.63663068172]
Centroid: CG[3.71766666667; 0.54554356057]
Coordinates of the circumscribed circle: U[5; -2.29217462426]
Coordinates of the inscribed circle: I[1.5; 0.77991937225]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.5254686157° = 169°31'29″ = 0.18328287167 rad
∠ B' = β' = 125.1099632195° = 125°5'59″ = 0.95881921787 rad
∠ C' = γ' = 65.37656816478° = 65°22'32″ = 2.00105717581 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 = 9 ; ; c = 10 ; ;

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

p = a+b+c = 2+9+10 = 21 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21 }{ 2 } = 10.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.5 * (10.5-2)(10.5-9)(10.5-10) } ; ; T = sqrt{ 66.94 } = 8.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.18 }{ 2 } = 8.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.18 }{ 9 } = 1.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.18 }{ 10 } = 1.64 ; ;

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**2-9**2-10**2 }{ 2 * 9 * 10 } ) = 10° 28'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-2**2-10**2 }{ 2 * 2 * 10 } ) = 54° 54'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10**2-2**2-9**2 }{ 2 * 9 * 2 } ) = 114° 37'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.18 }{ 10.5 } = 0.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 10° 28'31" } = 5.5 ; ;




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