Right triangle calculator (a,b)

Please enter two properties of the right triangle

Use symbols: a, b, c, A, B, h, T, p, r, R


You have entered cathetus a, cathetus b and angle γ.

Right scalene triangle.

Sides: a = 196   b = 264   c = 328.8043892921

Area: T = 25872
Perimeter: p = 788.8043892921
Semiperimeter: s = 394.4021946461

Angle ∠ A = α = 36.59110882674° = 36°35'28″ = 0.63986349672 rad
Angle ∠ B = β = 53.40989117326° = 53°24'32″ = 0.93221613596 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 264
Height: hb = 196
Height: hc = 157.3770399542

Median: ma = 281.6032556807
Median: mb = 236.3054887804
Median: mc = 164.402194646

Inradius: r = 65.59880535395
Circumradius: R = 164.402194646

Vertex coordinates: A[328.8043892921; 0] B[0; 0] C[116.836559966; 157.3770399542]
Centroid: CG[148.5466497527; 52.45767998474]
Coordinates of the circumscribed circle: U[164.402194646; 0]
Coordinates of the inscribed circle: I[130.402194646; 65.59880535395]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.4098911733° = 143°24'32″ = 0.63986349672 rad
∠ B' = β' = 126.5911088267° = 126°35'28″ = 0.93221613596 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a cathetus b angle γ

a = 196 ; ; b = 264 ; ; gamma = 90° ; ;

2. From cathetus a and cathetus b we calculate hypotenuse c - Pythagorean theorem:

c**2 = a**2+b**2 ; ; c = sqrt{ a**2+b**2 } = sqrt{ 196**2 + 264**2 } = 328.804 ; ;


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 = 196 ; ; b = 264 ; ; c = 328.8 ; ;

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

p = a+b+c = 196+264+328.8 = 788.8 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 788.8 }{ 2 } = 394.4 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 394.4 * (394.4-196)(394.4-264)(394.4-328.8) } ; ; T = sqrt{ 669360384 } = 25872 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25872 }{ 196 } = 264 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25872 }{ 264 } = 196 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25872 }{ 328.8 } = 157.37 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 196**2-264**2-328.8**2 }{ 2 * 264 * 328.8 } ) = 36° 35'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 264**2-196**2-328.8**2 }{ 2 * 196 * 328.8 } ) = 53° 24'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 328.8**2-196**2-264**2 }{ 2 * 264 * 196 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25872 }{ 394.4 } = 65.6 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 196 }{ 2 * sin 36° 35'28" } = 164.4 ; ;
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