22 25 25 triangle

Acute isosceles triangle.

Sides: a = 22   b = 25   c = 25

Area: T = 246.9499387527
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 52.20877622747° = 52°12'28″ = 0.91111973468 rad
Angle ∠ B = β = 63.89661188627° = 63°53'46″ = 1.11551976534 rad
Angle ∠ C = γ = 63.89661188627° = 63°53'46″ = 1.11551976534 rad

Height: ha = 22.45499443206
Height: hb = 19.75659510022
Height: hc = 19.75659510022

Median: ma = 22.45499443206
Median: mb = 19.95662020435
Median: mc = 19.95662020435

Inradius: r = 6.86597052091
Circumradius: R = 13.92198563496

Vertex coordinates: A[25; 0] B[0; 0] C[9.68; 19.75659510022]
Centroid: CG[11.56; 6.58553170007]
Coordinates of the circumscribed circle: U[12.5; 6.12547367938]
Coordinates of the inscribed circle: I[11; 6.86597052091]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.7922237725° = 127°47'32″ = 0.91111973468 rad
∠ B' = β' = 116.1043881137° = 116°6'14″ = 1.11551976534 rad
∠ C' = γ' = 116.1043881137° = 116°6'14″ = 1.11551976534 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 = 22 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 22+25+25 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-22)(36-25)(36-25) } ; ; T = sqrt{ 60984 } = 246.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 246.95 }{ 22 } = 22.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 246.95 }{ 25 } = 19.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 246.95 }{ 25 } = 19.76 ; ;

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{ 22**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 52° 12'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 63° 53'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-22**2-25**2 }{ 2 * 25 * 22 } ) = 63° 53'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 246.95 }{ 36 } = 6.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 52° 12'28" } = 13.92 ; ;




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