23 25 25 triangle

Acute isosceles triangle.

Sides: a = 23   b = 25   c = 25

Area: T = 255.2776688125
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 54.77442150053° = 54°46'27″ = 0.9565990397 rad
Angle ∠ B = β = 62.61328924973° = 62°36'46″ = 1.09328011283 rad
Angle ∠ C = γ = 62.61328924973° = 62°36'46″ = 1.09328011283 rad

Height: ha = 22.19879728804
Height: hb = 20.422213505
Height: hc = 20.422213505

Median: ma = 22.19879728804
Median: mb = 20.51221914968
Median: mc = 20.51221914968

Inradius: r = 6.99438818664
Circumradius: R = 14.078786205

Vertex coordinates: A[25; 0] B[0; 0] C[10.58; 20.422213505]
Centroid: CG[11.86; 6.807737835]
Coordinates of the circumscribed circle: U[12.5; 6.4765816543]
Coordinates of the inscribed circle: I[11.5; 6.99438818664]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.2265784995° = 125°13'33″ = 0.9565990397 rad
∠ B' = β' = 117.3877107503° = 117°23'14″ = 1.09328011283 rad
∠ C' = γ' = 117.3877107503° = 117°23'14″ = 1.09328011283 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 = 23 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 23+25+25 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-23)(36.5-25)(36.5-25) } ; ; T = sqrt{ 65166.19 } = 255.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 255.28 }{ 23 } = 22.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 255.28 }{ 25 } = 20.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 255.28 }{ 25 } = 20.42 ; ;

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{ 23**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 54° 46'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 62° 36'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-23**2-25**2 }{ 2 * 25 * 23 } ) = 62° 36'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 255.28 }{ 36.5 } = 6.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 54° 46'27" } = 14.08 ; ;




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