7 29 29 triangle

Acute isosceles triangle.

Sides: a = 7   b = 29   c = 29

Area: T = 100.7588064193
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 13.86438123952° = 13°51'50″ = 0.24219691732 rad
Angle ∠ B = β = 83.06880938024° = 83°4'5″ = 1.45498117402 rad
Angle ∠ C = γ = 83.06880938024° = 83°4'5″ = 1.45498117402 rad

Height: ha = 28.7888018341
Height: hb = 6.94988320133
Height: hc = 6.94988320133

Median: ma = 28.7888018341
Median: mb = 15.3221553446
Median: mc = 15.3221553446

Inradius: r = 3.1100248129
Circumradius: R = 14.6076771297

Vertex coordinates: A[29; 0] B[0; 0] C[0.84548275862; 6.94988320133]
Centroid: CG[9.94882758621; 2.31662773378]
Coordinates of the circumscribed circle: U[14.5; 1.7632886191]
Coordinates of the inscribed circle: I[3.5; 3.1100248129]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.1366187605° = 166°8'10″ = 0.24219691732 rad
∠ B' = β' = 96.93219061976° = 96°55'55″ = 1.45498117402 rad
∠ C' = γ' = 96.93219061976° = 96°55'55″ = 1.45498117402 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 = 29 ; ; c = 29 ; ;

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

p = a+b+c = 7+29+29 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-7)(32.5-29)(32.5-29) } ; ; T = sqrt{ 10152.19 } = 100.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 100.76 }{ 7 } = 28.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 100.76 }{ 29 } = 6.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 100.76 }{ 29 } = 6.95 ; ;

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**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 13° 51'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-7**2-29**2 }{ 2 * 7 * 29 } ) = 83° 4'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-7**2-29**2 }{ 2 * 29 * 7 } ) = 83° 4'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 100.76 }{ 32.5 } = 3.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 13° 51'50" } = 14.61 ; ;




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