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 and cathetus b.

Right scalene triangle.

Sides: a = 288   b = 175   c = 337

Area: T = 25200
Perimeter: p = 800
Semiperimeter: s = 400

Angle ∠ A = α = 58.71655070856° = 58°42'56″ = 1.02547789206 rad
Angle ∠ B = β = 31.28444929144° = 31°17'4″ = 0.54660174062 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 175
Height: hb = 288
Height: hc = 149.5554896142

Median: ma = 226.6329653841
Median: mb = 300.999875415
Median: mc = 168.5

Inradius: r = 63
Circumradius: R = 168.5

Vertex coordinates: A[337; 0] B[0; 0] C[246.125462908; 149.5554896142]
Centroid: CG[194.375487636; 49.85216320475]
Coordinates of the circumscribed circle: U[168.5; 0]
Coordinates of the inscribed circle: I[225; 63]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.2844492914° = 121°17'4″ = 1.02547789206 rad
∠ B' = β' = 148.7165507086° = 148°42'56″ = 0.54660174062 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

a = 288 ; ; b = 175 ; ;

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{ 288**2 + 175**2 } = 337 ; ;


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 = 288 ; ; b = 175 ; ; c = 337 ; ;

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

p = a+b+c = 288+175+337 = 800 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 800 }{ 2 } = 400 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 400 * (400-288)(400-175)(400-337) } ; ; T = sqrt{ 635040000 } = 25200 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25200 }{ 288 } = 175 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25200 }{ 175 } = 288 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25200 }{ 337 } = 149.55 ; ;

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{ 288**2-175**2-337**2 }{ 2 * 175 * 337 } ) = 58° 42'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 175**2-288**2-337**2 }{ 2 * 288 * 337 } ) = 31° 17'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 337**2-288**2-175**2 }{ 2 * 175 * 288 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25200 }{ 400 } = 63 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 288 }{ 2 * sin 58° 42'56" } = 168.5 ; ;
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