7 7 10 triangle

Obtuse isosceles triangle.

Sides: a = 7   b = 7   c = 10

Area: T = 24.49548974278
Perimeter: p = 24
Semiperimeter: s = 12

Angle ∠ A = α = 44.41553085972° = 44°24'55″ = 0.77551933733 rad
Angle ∠ B = β = 44.41553085972° = 44°24'55″ = 0.77551933733 rad
Angle ∠ C = γ = 91.16993828056° = 91°10'10″ = 1.5911205907 rad

Height: ha = 6.99985421222
Height: hb = 6.99985421222
Height: hc = 4.89989794856

Median: ma = 7.8989866919
Median: mb = 7.8989866919
Median: mc = 4.89989794856

Inradius: r = 2.04112414523
Circumradius: R = 5.00110415582

Vertex coordinates: A[10; 0] B[0; 0] C[5; 4.89989794856]
Centroid: CG[5; 1.63329931619]
Coordinates of the circumscribed circle: U[5; -0.10220620726]
Coordinates of the inscribed circle: I[5; 2.04112414523]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.5854691403° = 135°35'5″ = 0.77551933733 rad
∠ B' = β' = 135.5854691403° = 135°35'5″ = 0.77551933733 rad
∠ C' = γ' = 88.83106171944° = 88°49'50″ = 1.5911205907 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 = 7 ; ; c = 10 ; ;

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

p = a+b+c = 7+7+10 = 24 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24 }{ 2 } = 12 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12 * (12-7)(12-7)(12-10) } ; ; T = sqrt{ 600 } = 24.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24.49 }{ 7 } = 7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24.49 }{ 7 } = 7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24.49 }{ 10 } = 4.9 ; ;

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**2-7**2-10**2 }{ 2 * 7 * 10 } ) = 44° 24'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-7**2-10**2 }{ 2 * 7 * 10 } ) = 44° 24'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10**2-7**2-7**2 }{ 2 * 7 * 7 } ) = 91° 10'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24.49 }{ 12 } = 2.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 44° 24'55" } = 5 ; ;




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