5 16 16 triangle

Acute isosceles triangle.

Sides: a = 5   b = 16   c = 16

Area: T = 39.50987015732
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 17.97985986903° = 17°58'43″ = 0.3143785742 rad
Angle ∠ B = β = 81.01107006548° = 81°39″ = 1.41439034558 rad
Angle ∠ C = γ = 81.01107006548° = 81°39″ = 1.41439034558 rad

Height: ha = 15.80334806293
Height: hb = 4.93985876966
Height: hc = 4.93985876966

Median: ma = 15.80334806293
Median: mb = 8.74664278423
Median: mc = 8.74664278423

Inradius: r = 2.13656054904
Circumradius: R = 8.09994815638

Vertex coordinates: A[16; 0] B[0; 0] C[0.781125; 4.93985876966]
Centroid: CG[5.594375; 1.64661958989]
Coordinates of the circumscribed circle: U[8; 1.26655439943]
Coordinates of the inscribed circle: I[2.5; 2.13656054904]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.021140131° = 162°1'17″ = 0.3143785742 rad
∠ B' = β' = 98.98992993452° = 98°59'21″ = 1.41439034558 rad
∠ C' = γ' = 98.98992993452° = 98°59'21″ = 1.41439034558 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 = 16 ; ; c = 16 ; ;

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

p = a+b+c = 5+16+16 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-5)(18.5-16)(18.5-16) } ; ; T = sqrt{ 1560.94 } = 39.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.51 }{ 5 } = 15.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.51 }{ 16 } = 4.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.51 }{ 16 } = 4.94 ; ;

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{ 16**2+16**2-5**2 }{ 2 * 16 * 16 } ) = 17° 58'43" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5**2+16**2-16**2 }{ 2 * 5 * 16 } ) = 81° 39" ; ; gamma = 180° - alpha - beta = 180° - 17° 58'43" - 81° 39" = 81° 39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.51 }{ 18.5 } = 2.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 17° 58'43" } = 8.1 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 16**2 - 5**2 } }{ 2 } = 15.803 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 5**2 - 16**2 } }{ 2 } = 8.746 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 5**2 - 16**2 } }{ 2 } = 8.746 ; ;
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