Triangle calculator SAS

Please enter two sides of the triangle and the included angle
°


Obtuse isosceles triangle.

Sides: a = 5500   b = 5500   c = 9428.84403077232

Area: T = 13354582.3421991
Perimeter: p = 20428.8440307723
Semiperimeter: s = 10214.4220153862

Angle ∠ A = α = 31° = 0.54110520681 rad
Angle ∠ B = β = 31° = 0.54110520681 rad
Angle ∠ C = γ = 118° = 2.05994885174 rad

Height: ha = 4856.21217607241
Height: hb = 4856.21217607241
Height: hc = 2832.70994120053

Median: ma = 7212.07442352165
Median: mb = 7212.07442352165
Median: mc = 2832.70994120053

Inradius: r = 1307.42444196762
Circumradius: R = 5339.41110726285

Vertex coordinates: A[9428.84403077232; 0] B[0; 0] C[4714.42201538616; 2832.70994120053]
Centroid: CG[4714.42201538616; 944.23664706684]
Coordinates of the circumscribed circle: U[4714.42201538616; -2506.70216606232]
Coordinates of the inscribed circle: I[4714.42201538616; 1307.42444196762]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149° = 0.54110520681 rad
∠ B' = β' = 149° = 0.54110520681 rad
∠ C' = γ' = 62° = 2.05994885174 rad

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How did we calculate this triangle?

1. Calculation of the third side c of the triangle using a Law of Cosines

a = 5500 ; ; b = 5500 ; ; gamma = 118° ; ; ; ; c**2 = a**2+b**2 - 2ab cos gamma ; ; c = sqrt{ a**2+b**2 - 2ab cos gamma } ; ; c = sqrt{ 5500**2+5500**2 - 2 * 5500 * 5500 * cos(118° ) } ; ; c = 9428.84 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 5500 ; ; b = 5500 ; ; c = 9428.84 ; ;

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

p = a+b+c = 5500+5500+9428.84 = 20428.84 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20428.84 }{ 2 } = 10214.42 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10214.42 * (10214.42-5500)(10214.42-5500)(10214.42-9428.84) } ; ; T = sqrt{ 1.783 * 10**{ 14 } } = 13354582.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13354582.34 }{ 5500 } = 4856.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13354582.34 }{ 5500 } = 4856.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13354582.34 }{ 9428.84 } = 2832.71 ; ;

6. 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{ 5500**2+9428.84**2-5500**2 }{ 2 * 5500 * 9428.84 } ) = 31° ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5500**2+9428.84**2-5500**2 }{ 2 * 5500 * 9428.84 } ) = 31° ; ; gamma = 180° - alpha - beta = 180° - 31° - 31° = 118° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13354582.34 }{ 10214.42 } = 1307.42 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5500 }{ 2 * sin 31° } = 5339.41 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5500**2+2 * 9428.84**2 - 5500**2 } }{ 2 } = 7212.074 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9428.84**2+2 * 5500**2 - 5500**2 } }{ 2 } = 7212.074 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5500**2+2 * 5500**2 - 9428.84**2 } }{ 2 } = 2832.709 ; ;
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