16 25 29 triangle

Acute scalene triangle.

Sides: a = 16   b = 25   c = 29

Area: T = 199.7549843554
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 33.43879821579° = 33°26'17″ = 0.58436028839 rad
Angle ∠ B = β = 59.42880018247° = 59°25'41″ = 1.03772142997 rad
Angle ∠ C = γ = 87.13440160174° = 87°8'2″ = 1.521077547 rad

Height: ha = 24.96987304443
Height: hb = 15.98799874844
Height: hc = 13.77658512796

Median: ma = 25.86550343128
Median: mb = 19.80553023203
Median: mc = 15.17439909055

Inradius: r = 5.70771383873
Circumradius: R = 14.51881590553

Vertex coordinates: A[29; 0] B[0; 0] C[8.13879310345; 13.77658512796]
Centroid: CG[12.37993103448; 4.59219504265]
Coordinates of the circumscribed circle: U[14.5; 0.72659079528]
Coordinates of the inscribed circle: I[10; 5.70771383873]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.5622017842° = 146°33'43″ = 0.58436028839 rad
∠ B' = β' = 120.5721998175° = 120°34'19″ = 1.03772142997 rad
∠ C' = γ' = 92.86659839826° = 92°51'58″ = 1.521077547 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 = 25 ; ; c = 29 ; ;

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

p = a+b+c = 16+25+29 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-16)(35-25)(35-29) } ; ; T = sqrt{ 39900 } = 199.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 199.75 }{ 16 } = 24.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 199.75 }{ 25 } = 15.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 199.75 }{ 29 } = 13.78 ; ;

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**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 33° 26'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-16**2-29**2 }{ 2 * 16 * 29 } ) = 59° 25'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-16**2-25**2 }{ 2 * 25 * 16 } ) = 87° 8'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 199.75 }{ 35 } = 5.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 33° 26'17" } = 14.52 ; ;




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