Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 16   b = 25   c = 25

Area: T = 189.4843508517
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 37.32658497699° = 37°19'33″ = 0.65114589746 rad
Angle ∠ B = β = 71.33770751151° = 71°20'13″ = 1.24550668395 rad
Angle ∠ C = γ = 71.33770751151° = 71°20'13″ = 1.24550668395 rad

Height: ha = 23.68554385647
Height: hb = 15.15986806814
Height: hc = 15.15986806814

Median: ma = 23.68554385647
Median: mb = 16.86597153001
Median: mc = 16.86597153001

Inradius: r = 5.74219245005
Circumradius: R = 13.19437603413

Vertex coordinates: A[25; 0] B[0; 0] C[5.12; 15.15986806814]
Centroid: CG[10.04; 5.05328935605]
Coordinates of the circumscribed circle: U[12.5; 4.22220033092]
Coordinates of the inscribed circle: I[8; 5.74219245005]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.674415023° = 142°40'27″ = 0.65114589746 rad
∠ B' = β' = 108.6632924885° = 108°39'47″ = 1.24550668395 rad
∠ C' = γ' = 108.6632924885° = 108°39'47″ = 1.24550668395 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 = 16+25+25 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-16)(33-25)(33-25) } ; ; T = sqrt{ 35904 } = 189.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 189.48 }{ 16 } = 23.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 189.48 }{ 25 } = 15.16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 189.48 }{ 25 } = 15.16 ; ;

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{ 25**2+25**2-16**2 }{ 2 * 25 * 25 } ) = 37° 19'33" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16**2+25**2-25**2 }{ 2 * 16 * 25 } ) = 71° 20'13" ; ; gamma = 180° - alpha - beta = 180° - 37° 19'33" - 71° 20'13" = 71° 20'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 189.48 }{ 33 } = 5.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16 }{ 2 * sin 37° 19'33" } = 13.19 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 25**2 - 16**2 } }{ 2 } = 23.685 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 16**2 - 25**2 } }{ 2 } = 16.86 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 16**2 - 25**2 } }{ 2 } = 16.86 ; ;
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