10 23 23 triangle

Acute isosceles triangle.

Sides: a = 10   b = 23   c = 23

Area: T = 112.2549721603
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 25.11217155972° = 25°6'42″ = 0.4388282118 rad
Angle ∠ B = β = 77.44441422014° = 77°26'39″ = 1.35216552678 rad
Angle ∠ C = γ = 77.44441422014° = 77°26'39″ = 1.35216552678 rad

Height: ha = 22.45499443206
Height: hb = 9.76108453568
Height: hc = 9.76108453568

Median: ma = 22.45499443206
Median: mb = 13.5
Median: mc = 13.5

Inradius: r = 4.00989186287
Circumradius: R = 11.78217664143

Vertex coordinates: A[23; 0] B[0; 0] C[2.17439130435; 9.76108453568]
Centroid: CG[8.39113043478; 3.25436151189]
Coordinates of the circumscribed circle: U[11.5; 2.56112535683]
Coordinates of the inscribed circle: I[5; 4.00989186287]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.8888284403° = 154°53'18″ = 0.4388282118 rad
∠ B' = β' = 102.5565857799° = 102°33'21″ = 1.35216552678 rad
∠ C' = γ' = 102.5565857799° = 102°33'21″ = 1.35216552678 rad

Calculate another triangle




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 = 10 ; ; b = 23 ; ; c = 23 ; ;

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

p = a+b+c = 10+23+23 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-10)(28-23)(28-23) } ; ; T = sqrt{ 12600 } = 112.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 112.25 }{ 10 } = 22.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 112.25 }{ 23 } = 9.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 112.25 }{ 23 } = 9.76 ; ;

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{ 10**2-23**2-23**2 }{ 2 * 23 * 23 } ) = 25° 6'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-10**2-23**2 }{ 2 * 10 * 23 } ) = 77° 26'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-10**2-23**2 }{ 2 * 23 * 10 } ) = 77° 26'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 112.25 }{ 28 } = 4.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 25° 6'42" } = 11.78 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.