7 26 26 triangle

Acute isosceles triangle.

Sides: a = 7   b = 26   c = 26

Area: T = 90.17217111959
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 15.47327600799° = 15°28'22″ = 0.27700506078 rad
Angle ∠ B = β = 82.264361996° = 82°15'49″ = 1.43657710229 rad
Angle ∠ C = γ = 82.264361996° = 82°15'49″ = 1.43657710229 rad

Height: ha = 25.7633346056
Height: hb = 6.93662854766
Height: hc = 6.93662854766

Median: ma = 25.7633346056
Median: mb = 13.91104277432
Median: mc = 13.91104277432

Inradius: r = 3.05766681761
Circumradius: R = 13.11994138861

Vertex coordinates: A[26; 0] B[0; 0] C[0.94223076923; 6.93662854766]
Centroid: CG[8.98107692308; 2.31220951589]
Coordinates of the circumscribed circle: U[13; 1.76660749462]
Coordinates of the inscribed circle: I[3.5; 3.05766681761]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.527723992° = 164°31'38″ = 0.27700506078 rad
∠ B' = β' = 97.736638004° = 97°44'11″ = 1.43657710229 rad
∠ C' = γ' = 97.736638004° = 97°44'11″ = 1.43657710229 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 = 7 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 7+26+26 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-7)(29.5-26)(29.5-26) } ; ; T = sqrt{ 8130.94 } = 90.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 90.17 }{ 7 } = 25.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 90.17 }{ 26 } = 6.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 90.17 }{ 26 } = 6.94 ; ;

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{ 7**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 15° 28'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-7**2-26**2 }{ 2 * 7 * 26 } ) = 82° 15'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-7**2-26**2 }{ 2 * 26 * 7 } ) = 82° 15'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 90.17 }{ 29.5 } = 3.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 15° 28'22" } = 13.12 ; ;




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