Isosceles triangle calculator (a,b)

Please enter two properties of the isosceles triangle

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


You have entered side a and b.

Acute isosceles triangle.

Sides: a = 142   b = 142   c = 190

Area: T = 10026.43987995
Perimeter: p = 474
Semiperimeter: s = 237

Angle ∠ A = α = 48.00989830931° = 48°32″ = 0.83879148255 rad
Angle ∠ B = β = 48.00989830931° = 48°32″ = 0.83879148255 rad
Angle ∠ C = γ = 83.98220338138° = 83°58'55″ = 1.46657630026 rad

Height: ha = 141.217744788
Height: hb = 141.217744788
Height: hc = 105.5411461047

Median: ma = 151.9577230825
Median: mb = 151.9577230825
Median: mc = 105.5411461047

Inradius: r = 42.3065648943
Circumradius: R = 95.52664395618

Vertex coordinates: A[190; 0] B[0; 0] C[95; 105.5411461047]
Centroid: CG[95; 35.18804870158]
Coordinates of the circumscribed circle: U[95; 10.01550214855]
Coordinates of the inscribed circle: I[95; 42.3065648943]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.9911016907° = 131°59'28″ = 0.83879148255 rad
∠ B' = β' = 131.9911016907° = 131°59'28″ = 0.83879148255 rad
∠ C' = γ' = 96.01879661862° = 96°1'5″ = 1.46657630026 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 = 142 ; ; b = 142 ; ; c = 190 ; ;

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

p = a+b+c = 142+142+190 = 474 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 474 }{ 2 } = 237 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 237 * (237-142)(237-142)(237-190) } ; ; T = sqrt{ 100529475 } = 10026.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10026.44 }{ 142 } = 141.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10026.44 }{ 142 } = 141.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10026.44 }{ 190 } = 105.54 ; ;

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{ 142**2-142**2-190**2 }{ 2 * 142 * 190 } ) = 48° 32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 142**2-142**2-190**2 }{ 2 * 142 * 190 } ) = 48° 32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 190**2-142**2-142**2 }{ 2 * 142 * 142 } ) = 83° 58'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10026.44 }{ 237 } = 42.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 142 }{ 2 * sin 48° 32" } = 95.53 ; ;




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