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.

Obtuse isosceles triangle.

Sides: a = 170   b = 170   c = 295

Area: T = 12466.80443595
Perimeter: p = 635
Semiperimeter: s = 317.5

Angle ∠ A = α = 29.81436467865° = 29°48'49″ = 0.52203462985 rad
Angle ∠ B = β = 29.81436467865° = 29°48'49″ = 0.52203462985 rad
Angle ∠ C = γ = 120.3732706427° = 120°22'22″ = 2.10109000567 rad

Height: ha = 146.6688286582
Height: hb = 146.6688286582
Height: hc = 84.52107075219

Median: ma = 225.2549861265
Median: mb = 225.2549861265
Median: mc = 84.52107075219

Inradius: r = 39.26655255417
Circumradius: R = 170.9644020814

Vertex coordinates: A[295; 0] B[0; 0] C[147.5; 84.52107075219]
Centroid: CG[147.5; 28.1743569174]
Coordinates of the circumscribed circle: U[147.5; -86.44333132923]
Coordinates of the inscribed circle: I[147.5; 39.26655255417]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.1866353214° = 150°11'11″ = 0.52203462985 rad
∠ B' = β' = 150.1866353214° = 150°11'11″ = 0.52203462985 rad
∠ C' = γ' = 59.6277293573° = 59°37'38″ = 2.10109000567 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 = 170 ; ; b = 170 ; ; c = 295 ; ;

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

p = a+b+c = 170+170+295 = 635 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 635 }{ 2 } = 317.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 317.5 * (317.5-170)(317.5-170)(317.5-295) } ; ; T = sqrt{ 155421210.94 } = 12466.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12466.8 }{ 170 } = 146.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12466.8 }{ 170 } = 146.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12466.8 }{ 295 } = 84.52 ; ;

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{ 170**2-170**2-295**2 }{ 2 * 170 * 295 } ) = 29° 48'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 170**2-170**2-295**2 }{ 2 * 170 * 295 } ) = 29° 48'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 295**2-170**2-170**2 }{ 2 * 170 * 170 } ) = 120° 22'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12466.8 }{ 317.5 } = 39.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 170 }{ 2 * sin 29° 48'49" } = 170.96 ; ;




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