2 10 10 triangle

Acute isosceles triangle.

Sides: a = 2   b = 10   c = 10

Area: T = 9.95498743711
Perimeter: p = 22
Semiperimeter: s = 11

Angle ∠ A = α = 11.47883409545° = 11°28'42″ = 0.22003348423 rad
Angle ∠ B = β = 84.26108295227° = 84°15'39″ = 1.47106289056 rad
Angle ∠ C = γ = 84.26108295227° = 84°15'39″ = 1.47106289056 rad

Height: ha = 9.95498743711
Height: hb = 1.99899748742
Height: hc = 1.99899748742

Median: ma = 9.95498743711
Median: mb = 5.19661524227
Median: mc = 5.19661524227

Inradius: r = 0.90545340337
Circumradius: R = 5.02551890763

Vertex coordinates: A[10; 0] B[0; 0] C[0.2; 1.99899748742]
Centroid: CG[3.4; 0.66333249581]
Coordinates of the circumscribed circle: U[5; 0.50325189076]
Coordinates of the inscribed circle: I[1; 0.90545340337]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.5221659045° = 168°31'18″ = 0.22003348423 rad
∠ B' = β' = 95.73991704773° = 95°44'21″ = 1.47106289056 rad
∠ C' = γ' = 95.73991704773° = 95°44'21″ = 1.47106289056 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 = 10 ; ;

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

p = a+b+c = 2+10+10 = 22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22 }{ 2 } = 11 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11 * (11-2)(11-10)(11-10) } ; ; T = sqrt{ 99 } = 9.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9.95 }{ 2 } = 9.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9.95 }{ 10 } = 1.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9.95 }{ 10 } = 1.99 ; ;

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**2-10**2 }{ 2 * 10 * 10 } ) = 11° 28'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-2**2-10**2 }{ 2 * 2 * 10 } ) = 84° 15'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10**2-2**2-10**2 }{ 2 * 10 * 2 } ) = 84° 15'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9.95 }{ 11 } = 0.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 11° 28'42" } = 5.03 ; ;




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