5 7 7 triangle

Acute isosceles triangle.

Sides: a = 5   b = 7   c = 7

Area: T = 16.34658710383
Perimeter: p = 19
Semiperimeter: s = 9.5

Angle ∠ A = α = 41.85496648553° = 41°50'59″ = 0.73304144426 rad
Angle ∠ B = β = 69.07551675724° = 69°4'31″ = 1.20655891055 rad
Angle ∠ C = γ = 69.07551675724° = 69°4'31″ = 1.20655891055 rad

Height: ha = 6.53883484153
Height: hb = 4.67702488681
Height: hc = 4.67702488681

Median: ma = 6.53883484153
Median: mb = 4.97549371855
Median: mc = 4.97549371855

Inradius: r = 1.7210618004
Circumradius: R = 3.74771236532

Vertex coordinates: A[7; 0] B[0; 0] C[1.78657142857; 4.67702488681]
Centroid: CG[2.92985714286; 1.55767496227]
Coordinates of the circumscribed circle: U[3.5; 1.33882584476]
Coordinates of the inscribed circle: I[2.5; 1.7210618004]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.1550335145° = 138°9'1″ = 0.73304144426 rad
∠ B' = β' = 110.9254832428° = 110°55'29″ = 1.20655891055 rad
∠ C' = γ' = 110.9254832428° = 110°55'29″ = 1.20655891055 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 = 5 ; ; b = 7 ; ; c = 7 ; ;

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

p = a+b+c = 5+7+7 = 19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19 }{ 2 } = 9.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.5 * (9.5-5)(9.5-7)(9.5-7) } ; ; T = sqrt{ 267.19 } = 16.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.35 }{ 5 } = 6.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.35 }{ 7 } = 4.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.35 }{ 7 } = 4.67 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 7**2+7**2-5**2 }{ 2 * 7 * 7 } ) = 41° 50'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5**2+7**2-7**2 }{ 2 * 5 * 7 } ) = 69° 4'31" ; ; gamma = 180° - alpha - beta = 180° - 41° 50'59" - 69° 4'31" = 69° 4'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.35 }{ 9.5 } = 1.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 41° 50'59" } = 3.75 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7**2+2 * 7**2 - 5**2 } }{ 2 } = 6.538 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7**2+2 * 5**2 - 7**2 } }{ 2 } = 4.975 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7**2+2 * 5**2 - 7**2 } }{ 2 } = 4.975 ; ;
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