Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 16   b = 16   c = 29

Area: T = 98.07661821239
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 25.00878332347° = 25°28″ = 0.43664690287 rad
Angle ∠ B = β = 25.00878332347° = 25°28″ = 0.43664690287 rad
Angle ∠ C = γ = 129.9844333531° = 129°59'4″ = 2.26986545961 rad

Height: ha = 12.26595227655
Height: hb = 12.26595227655
Height: hc = 6.76438746292

Median: ma = 22.01113607031
Median: mb = 22.01113607031
Median: mc = 6.76438746292

Inradius: r = 3.21656125287
Circumradius: R = 18.92440645364

Vertex coordinates: A[29; 0] B[0; 0] C[14.5; 6.76438746292]
Centroid: CG[14.5; 2.25546248764]
Coordinates of the circumscribed circle: U[14.5; -12.16601899072]
Coordinates of the inscribed circle: I[14.5; 3.21656125287]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.9922166765° = 154°59'32″ = 0.43664690287 rad
∠ B' = β' = 154.9922166765° = 154°59'32″ = 0.43664690287 rad
∠ C' = γ' = 50.01656664694° = 50°56″ = 2.26986545961 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+16+29 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-16)(30.5-16)(30.5-29) } ; ; T = sqrt{ 9618.94 } = 98.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 98.08 }{ 16 } = 12.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 98.08 }{ 16 } = 12.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 98.08 }{ 29 } = 6.76 ; ;

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+29**2-16**2 }{ 2 * 16 * 29 } ) = 25° 28" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16**2+29**2-16**2 }{ 2 * 16 * 29 } ) = 25° 28" ; ; gamma = 180° - alpha - beta = 180° - 25° 28" - 25° 28" = 129° 59'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 98.08 }{ 30.5 } = 3.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16 }{ 2 * sin 25° 28" } = 18.92 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 29**2 - 16**2 } }{ 2 } = 22.011 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 16**2 - 16**2 } }{ 2 } = 22.011 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 16**2 - 29**2 } }{ 2 } = 6.764 ; ;
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