Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 18   b = 18   c = 24

Area: T = 160.997689438
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 48.19896851042° = 48°11'23″ = 0.84110686706 rad
Angle ∠ B = β = 48.19896851042° = 48°11'23″ = 0.84110686706 rad
Angle ∠ C = γ = 83.62106297916° = 83°37'14″ = 1.45994553125 rad

Height: ha = 17.889854382
Height: hb = 17.889854382
Height: hc = 13.4166407865

Median: ma = 19.20993727123
Median: mb = 19.20993727123
Median: mc = 13.4166407865

Inradius: r = 5.3676563146
Circumradius: R = 12.07547670785

Vertex coordinates: A[24; 0] B[0; 0] C[12; 13.4166407865]
Centroid: CG[12; 4.4722135955]
Coordinates of the circumscribed circle: U[12; 1.34216407865]
Coordinates of the inscribed circle: I[12; 5.3676563146]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.8110314896° = 131°48'37″ = 0.84110686706 rad
∠ B' = β' = 131.8110314896° = 131°48'37″ = 0.84110686706 rad
∠ C' = γ' = 96.37993702084° = 96°22'46″ = 1.45994553125 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 = 18+18+24 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-18)(30-18)(30-24) } ; ; T = sqrt{ 25920 } = 161 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 161 }{ 18 } = 17.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 161 }{ 18 } = 17.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 161 }{ 24 } = 13.42 ; ;

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{ 18**2+24**2-18**2 }{ 2 * 18 * 24 } ) = 48° 11'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18**2+24**2-18**2 }{ 2 * 18 * 24 } ) = 48° 11'23" ; ; gamma = 180° - alpha - beta = 180° - 48° 11'23" - 48° 11'23" = 83° 37'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 161 }{ 30 } = 5.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 18 }{ 2 * sin 48° 11'23" } = 12.07 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 24**2 - 18**2 } }{ 2 } = 19.209 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 18**2 - 18**2 } }{ 2 } = 19.209 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 18**2 - 24**2 } }{ 2 } = 13.416 ; ;
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