10 10 14 triangle

Acute isosceles triangle.

Sides: a = 10   b = 10   c = 14

Area: T = 49.99899989998
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 45.57329959992° = 45°34'23″ = 0.79553988302 rad
Angle ∠ B = β = 45.57329959992° = 45°34'23″ = 0.79553988302 rad
Angle ∠ C = γ = 88.85440080016° = 88°51'14″ = 1.55107949932 rad

Height: ha = 9.99879998
Height: hb = 9.99879998
Height: hc = 7.14114284285

Median: ma = 11.09105365064
Median: mb = 11.09105365064
Median: mc = 7.14114284285

Inradius: r = 2.94105881765
Circumradius: R = 7.00114004201

Vertex coordinates: A[14; 0] B[0; 0] C[7; 7.14114284285]
Centroid: CG[7; 2.38804761428]
Coordinates of the circumscribed circle: U[7; 0.14400280084]
Coordinates of the inscribed circle: I[7; 2.94105881765]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.4277004001° = 134°25'37″ = 0.79553988302 rad
∠ B' = β' = 134.4277004001° = 134°25'37″ = 0.79553988302 rad
∠ C' = γ' = 91.14659919984° = 91°8'46″ = 1.55107949932 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 = 10 ; ; b = 10 ; ; c = 14 ; ;

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

p = a+b+c = 10+10+14 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-10)(17-10)(17-14) } ; ; T = sqrt{ 2499 } = 49.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 49.99 }{ 10 } = 10 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 49.99 }{ 10 } = 10 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 49.99 }{ 14 } = 7.14 ; ;

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{ 10**2-10**2-14**2 }{ 2 * 10 * 14 } ) = 45° 34'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-10**2-14**2 }{ 2 * 10 * 14 } ) = 45° 34'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-10**2-10**2 }{ 2 * 10 * 10 } ) = 88° 51'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 49.99 }{ 17 } = 2.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 45° 34'23" } = 7 ; ;




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