Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 4   b = 7   c = 7

Area: T = 13.4166407865
Perimeter: p = 18
Semiperimeter: s = 9

Angle ∠ A = α = 33.2033099198° = 33°12'11″ = 0.58795034029 rad
Angle ∠ B = β = 73.3988450401° = 73°23'54″ = 1.28110446254 rad
Angle ∠ C = γ = 73.3988450401° = 73°23'54″ = 1.28110446254 rad

Height: ha = 6.70882039325
Height: hb = 3.833325939
Height: hc = 3.833325939

Median: ma = 6.70882039325
Median: mb = 4.5
Median: mc = 4.5

Inradius: r = 1.4910711985
Circumradius: R = 3.65222443632

Vertex coordinates: A[7; 0] B[0; 0] C[1.14328571429; 3.833325939]
Centroid: CG[2.71442857143; 1.278775313]
Coordinates of the circumscribed circle: U[3.5; 1.04334983895]
Coordinates of the inscribed circle: I[2; 1.4910711985]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.7976900802° = 146°47'49″ = 0.58795034029 rad
∠ B' = β' = 106.6021549599° = 106°36'6″ = 1.28110446254 rad
∠ C' = γ' = 106.6021549599° = 106°36'6″ = 1.28110446254 rad

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How did we calculate this triangle?

a = 4 ; ; b = 7 ; ; c = 7 ; ;

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

p = a+b+c = 4+7+7 = 18 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18 }{ 2 } = 9 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9 * (9-4)(9-7)(9-7) } ; ; T = sqrt{ 180 } = 13.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.42 }{ 4 } = 6.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.42 }{ 7 } = 3.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.42 }{ 7 } = 3.83 ; ;

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{ 4**2-7**2-7**2 }{ 2 * 7 * 7 } ) = 33° 12'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7**2-4**2-7**2 }{ 2 * 4 * 7 } ) = 73° 23'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7**2-4**2-7**2 }{ 2 * 7 * 4 } ) = 73° 23'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.42 }{ 9 } = 1.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 33° 12'11" } = 3.65 ; ;

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