Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and angle γ.

Right isosceles triangle.

Sides: a = 280   b = 280   c = 395.9879797464

Area: T = 39200
Perimeter: p = 955.9879797465
Semiperimeter: s = 477.9989898732

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 280
Height: hb = 280
Height: hc = 197.9989898732

Median: ma = 313.054951685
Median: mb = 313.054951685
Median: mc = 197.9989898732

Inradius: r = 82.01101012678
Circumradius: R = 197.9989898732

Vertex coordinates: A[395.9879797464; 0] B[0; 0] C[197.9989898732; 197.9989898732]
Centroid: CG[197.9989898732; 65.99766329107]
Coordinates of the circumscribed circle: U[197.9989898732; 0]
Coordinates of the inscribed circle: I[197.9989898732; 82.01101012678]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and angle γ.

a = 280 ; ; b = 280 ; ; gamma = 90° ; ;

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

c**2 = a**2+b**2 - 2ab cos gamma ; ; c = sqrt{ a**2+b**2 - 2ab cos gamma } ; ; c = sqrt{ 280**2+280**2 - 2 * 280 * 280 * cos 90° } ; ; c = 395.98 ; ;
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 = 280 ; ; b = 280 ; ; c = 395.98 ; ;

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

p = a+b+c = 280+280+395.98 = 955.98 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 955.98 }{ 2 } = 477.99 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 477.99 * (477.99-280)(477.99-280)(477.99-395.98) } ; ; T = sqrt{ 1536640000 } = 39200 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39200 }{ 280 } = 280 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39200 }{ 280 } = 280 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39200 }{ 395.98 } = 197.99 ; ;

7. 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{ 280**2+395.98**2-280**2 }{ 2 * 280 * 395.98 } ) = 45° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 280**2+395.98**2-280**2 }{ 2 * 280 * 395.98 } ) = 45° ; ; gamma = 180° - alpha - beta = 180° - 45° - 45° = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39200 }{ 477.99 } = 82.01 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 280 }{ 2 * sin 45° } = 197.99 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 280**2+2 * 395.98**2 - 280**2 } }{ 2 } = 313.05 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 395.98**2+2 * 280**2 - 280**2 } }{ 2 } = 313.05 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 280**2+2 * 280**2 - 395.98**2 } }{ 2 } = 197.99 ; ;
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