Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 1   b = 3   c = 3

Area: T = 1.47990199458
Perimeter: p = 7
Semiperimeter: s = 3.5

Angle ∠ A = α = 19.18881364537° = 19°11'17″ = 0.33548961584 rad
Angle ∠ B = β = 80.40659317731° = 80°24'21″ = 1.40333482476 rad
Angle ∠ C = γ = 80.40659317731° = 80°24'21″ = 1.40333482476 rad

Height: ha = 2.95880398915
Height: hb = 0.98660132972
Height: hc = 0.98660132972

Median: ma = 2.95880398915
Median: mb = 1.65883123952
Median: mc = 1.65883123952

Inradius: r = 0.42325771274
Circumradius: R = 1.52112776585

Vertex coordinates: A[3; 0] B[0; 0] C[0.16766666667; 0.98660132972]
Centroid: CG[1.05655555556; 0.32986710991]
Coordinates of the circumscribed circle: U[1.5; 0.25435462764]
Coordinates of the inscribed circle: I[0.5; 0.42325771274]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.8121863546° = 160°48'43″ = 0.33548961584 rad
∠ B' = β' = 99.59440682269° = 99°35'39″ = 1.40333482476 rad
∠ C' = γ' = 99.59440682269° = 99°35'39″ = 1.40333482476 rad

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How did we calculate this triangle?

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

p = a+b+c = 1+3+3 = 7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7 }{ 2 } = 3.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.5 * (3.5-1)(3.5-3)(3.5-3) } ; ; T = sqrt{ 2.19 } = 1.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.48 }{ 1 } = 2.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.48 }{ 3 } = 0.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.48 }{ 3 } = 0.99 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 3**2+3**2-1**2 }{ 2 * 3 * 3 } ) = 19° 11'17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1**2+3**2-3**2 }{ 2 * 1 * 3 } ) = 80° 24'21" ; ; gamma = 180° - alpha - beta = 180° - 19° 11'17" - 80° 24'21" = 80° 24'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.48 }{ 3.5 } = 0.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1 }{ 2 * sin 19° 11'17" } = 1.52 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3**2+2 * 3**2 - 1**2 } }{ 2 } = 2.958 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3**2+2 * 1**2 - 3**2 } }{ 2 } = 1.658 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3**2+2 * 1**2 - 3**2 } }{ 2 } = 1.658 ; ;
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