Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 1   b = 16   c = 16

Area: T = 7.99660927959
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 3.58215693187° = 3°34'54″ = 0.0632510177 rad
Angle ∠ B = β = 88.20992153407° = 88°12'33″ = 1.54395412383 rad
Angle ∠ C = γ = 88.20992153407° = 88°12'33″ = 1.54395412383 rad

Height: ha = 15.99221855917
Height: hb = 10.9995115995
Height: hc = 10.9995115995

Median: ma = 15.99221855917
Median: mb = 8.03111892021
Median: mc = 8.03111892021

Inradius: r = 0.48546116846
Circumradius: R = 8.00439091134

Vertex coordinates: A[16; 0] B[0; 0] C[0.031125; 10.9995115995]
Centroid: CG[5.344375; 0.33331705332]
Coordinates of the circumscribed circle: U[8; 0.25501221598]
Coordinates of the inscribed circle: I[0.5; 0.48546116846]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.4188430681° = 176°25'6″ = 0.0632510177 rad
∠ B' = β' = 91.79107846593° = 91°47'27″ = 1.54395412383 rad
∠ C' = γ' = 91.79107846593° = 91°47'27″ = 1.54395412383 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+16+16 = 33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33 }{ 2 } = 16.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.5 * (16.5-1)(16.5-16)(16.5-16) } ; ; T = sqrt{ 63.94 } = 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 * 8 }{ 1 } = 15.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8 }{ 16 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8 }{ 16 } = 1 ; ;

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{ 16**2+16**2-1**2 }{ 2 * 16 * 16 } ) = 3° 34'54" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1**2+16**2-16**2 }{ 2 * 1 * 16 } ) = 88° 12'33" ; ; gamma = 180° - alpha - beta = 180° - 3° 34'54" - 88° 12'33" = 88° 12'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8 }{ 16.5 } = 0.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1 }{ 2 * sin 3° 34'54" } = 8 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 16**2 - 1**2 } }{ 2 } = 15.992 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 1**2 - 16**2 } }{ 2 } = 8.031 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 1**2 - 16**2 } }{ 2 } = 8.031 ; ;
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