Isosceles triangle calculator (p)

Please enter two properties of the isosceles triangle

Use symbols: a, b, h, T, p, A, B, C, r, R


You have entered perimeter p and angle γ.

Obtuse isosceles triangle.

Sides: a = 78.80993197013   b = 78.80993197013   c = 113.3811360598

Area: T = 3103.563267695
Perimeter: p = 271
Semiperimeter: s = 135.5

Angle ∠ A = α = 44° = 0.76879448709 rad
Angle ∠ B = β = 44° = 0.76879448709 rad
Angle ∠ C = γ = 92° = 1.60657029118 rad

Height: ha = 78.76113111931
Height: hb = 78.76113111931
Height: hc = 54.74655536007

Median: ma = 89.33330492226
Median: mb = 89.33330492226
Median: mc = 54.74655536007

Inradius: r = 22.90545216011
Circumradius: R = 56.72552357797

Vertex coordinates: A[113.3811360598; 0] B[0; 0] C[56.69106802987; 54.74655536007]
Centroid: CG[56.69106802987; 18.24985178669]
Coordinates of the circumscribed circle: U[56.69106802987; -1.9879682179]
Coordinates of the inscribed circle: I[56.69106802987; 22.90545216011]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136° = 0.76879448709 rad
∠ B' = β' = 136° = 0.76879448709 rad
∠ C' = γ' = 88° = 1.60657029118 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 = 78.81 ; ; b = 78.81 ; ; c = 113.38 ; ;

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

p = a+b+c = 78.81+78.81+113.38 = 271 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 271 }{ 2 } = 135.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 135.5 * (135.5-78.81)(135.5-78.81)(135.5-113.38) } ; ; T = sqrt{ 9632101.29 } = 3103.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3103.56 }{ 78.81 } = 78.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3103.56 }{ 78.81 } = 78.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3103.56 }{ 113.38 } = 54.75 ; ;

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{ 78.81**2-78.81**2-113.38**2 }{ 2 * 78.81 * 113.38 } ) = 44° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 78.81**2-78.81**2-113.38**2 }{ 2 * 78.81 * 113.38 } ) = 44° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 113.38**2-78.81**2-78.81**2 }{ 2 * 78.81 * 78.81 } ) = 92° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3103.56 }{ 135.5 } = 22.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 78.81 }{ 2 * sin 44° } = 56.73 ; ;




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