23 23 25 triangle

Acute isosceles triangle.

Sides: a = 23   b = 23   c = 25

Area: T = 241.3344182204
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 57.07992654719° = 57°4'45″ = 0.99662211171 rad
Angle ∠ B = β = 57.07992654719° = 57°4'45″ = 0.99662211171 rad
Angle ∠ C = γ = 65.84114690562° = 65°50'29″ = 1.14991504194 rad

Height: ha = 20.98655810612
Height: hb = 20.98655810612
Height: hc = 19.30767345763

Median: ma = 21.0899096709
Median: mb = 21.0899096709
Median: mc = 19.30767345763

Inradius: r = 6.79881459776
Circumradius: R = 13.7699882751

Vertex coordinates: A[25; 0] B[0; 0] C[12.5; 19.30767345763]
Centroid: CG[12.5; 6.43655781921]
Coordinates of the circumscribed circle: U[12.5; 5.60768518253]
Coordinates of the inscribed circle: I[12.5; 6.79881459776]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.9210734528° = 122°55'15″ = 0.99662211171 rad
∠ B' = β' = 122.9210734528° = 122°55'15″ = 0.99662211171 rad
∠ C' = γ' = 114.1598530944° = 114°9'31″ = 1.14991504194 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 = 23 ; ; c = 25 ; ;

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

p = a+b+c = 23+23+25 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-23)(35.5-23)(35.5-25) } ; ; T = sqrt{ 58242.19 } = 241.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 241.33 }{ 23 } = 20.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 241.33 }{ 23 } = 20.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 241.33 }{ 25 } = 19.31 ; ;

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**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 57° 4'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 57° 4'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-23**2-23**2 }{ 2 * 23 * 23 } ) = 65° 50'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 241.33 }{ 35.5 } = 6.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 57° 4'45" } = 13.7 ; ;




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