16 16 25 triangle

Obtuse isosceles triangle.

Sides: a = 16   b = 16   c = 25

Area: T = 124.8443652221
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 38.62548328731° = 38°37'29″ = 0.67441305067 rad
Angle ∠ B = β = 38.62548328731° = 38°37'29″ = 0.67441305067 rad
Angle ∠ C = γ = 102.7550334254° = 102°45'1″ = 1.79333316403 rad

Height: ha = 15.60554565277
Height: hb = 15.60554565277
Height: hc = 9.98774921777

Median: ma = 19.40436079119
Median: mb = 19.40436079119
Median: mc = 9.98774921777

Inradius: r = 4.38804790253
Circumradius: R = 12.81660300626

Vertex coordinates: A[25; 0] B[0; 0] C[12.5; 9.98774921777]
Centroid: CG[12.5; 3.32991640592]
Coordinates of the circumscribed circle: U[12.5; -2.82985378849]
Coordinates of the inscribed circle: I[12.5; 4.38804790253]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.3755167127° = 141°22'31″ = 0.67441305067 rad
∠ B' = β' = 141.3755167127° = 141°22'31″ = 0.67441305067 rad
∠ C' = γ' = 77.25496657461° = 77°14'59″ = 1.79333316403 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 = 16 ; ; b = 16 ; ; c = 25 ; ;

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

p = a+b+c = 16+16+25 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-16)(28.5-16)(28.5-25) } ; ; T = sqrt{ 15585.94 } = 124.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 124.84 }{ 16 } = 15.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 124.84 }{ 16 } = 15.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 124.84 }{ 25 } = 9.99 ; ;

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{ 16**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 38° 37'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 38° 37'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 102° 45'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 124.84 }{ 28.5 } = 4.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 38° 37'29" } = 12.82 ; ;




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