40 40 48 triangle

Acute isosceles triangle.

Sides: a = 40   b = 40   c = 48

Area: T = 768
Perimeter: p = 128
Semiperimeter: s = 64

Angle ∠ A = α = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 73.74397952917° = 73°44'23″ = 1.28770022176 rad

Height: ha = 38.4
Height: hb = 38.4
Height: hc = 32

Median: ma = 39.39554312072
Median: mb = 39.39554312072
Median: mc = 32

Inradius: r = 12
Circumradius: R = 25

Vertex coordinates: A[48; 0] B[0; 0] C[24; 32]
Centroid: CG[24; 10.66766666667]
Coordinates of the circumscribed circle: U[24; 7]
Coordinates of the inscribed circle: I[24; 12]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 106.2660204708° = 106°15'37″ = 1.28770022176 rad

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How did we calculate this triangle?

a = 40 ; ; b = 40 ; ; c = 48 ; ;

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

p = a+b+c = 40+40+48 = 128 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 128 }{ 2 } = 64 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 64 * (64-40)(64-40)(64-48) } ; ; T = sqrt{ 589824 } = 768 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 768 }{ 40 } = 38.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 768 }{ 40 } = 38.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 768 }{ 48 } = 32 ; ;

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{ 40**2-40**2-48**2 }{ 2 * 40 * 48 } ) = 53° 7'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 40**2-40**2-48**2 }{ 2 * 40 * 48 } ) = 53° 7'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 48**2-40**2-40**2 }{ 2 * 40 * 40 } ) = 73° 44'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 768 }{ 64 } = 12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 40 }{ 2 * sin 53° 7'48" } = 25 ; ;




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