Right triangle calculator (b,c)

Please enter two properties of the right triangle

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


You have entered cathetus b and hypotenuse c.

Right scalene triangle.

Sides: a = 335.4110196625   b = 100   c = 350

Area: T = 16770.51098312
Perimeter: p = 785.4110196625
Semiperimeter: s = 392.7055098313

Angle ∠ A = α = 73.3988450401° = 73°23'54″ = 1.28110446254 rad
Angle ∠ B = β = 16.6021549599° = 16°36'6″ = 0.29897517014 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 100
Height: hb = 335.4110196625
Height: hc = 95.831148475

Median: ma = 195.2566241898
Median: mb = 339.1166499156
Median: mc = 175

Inradius: r = 42.70550983125
Circumradius: R = 175

Vertex coordinates: A[350; 0] B[0; 0] C[321.4298571429; 95.831148475]
Centroid: CG[223.810952381; 31.944382825]
Coordinates of the circumscribed circle: U[175; 0]
Coordinates of the inscribed circle: I[292.7055098313; 42.70550983125]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 106.6021549599° = 106°36'6″ = 1.28110446254 rad
∠ B' = β' = 163.3988450401° = 163°23'54″ = 0.29897517014 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus b and hypotenuse c

b = 100 ; ; c = 350 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 350**2 - 100**2 } = 335.41 ; ;


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 = 335.41 ; ; b = 100 ; ; c = 350 ; ;

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

p = a+b+c = 335.41+100+350 = 785.41 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 785.41 }{ 2 } = 392.71 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 392.71 * (392.71-335.41)(392.71-100)(392.71-350) } ; ; T = sqrt{ 281250000 } = 16770.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16770.51 }{ 335.41 } = 100 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16770.51 }{ 100 } = 335.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16770.51 }{ 350 } = 95.83 ; ;

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{ 335.41**2-100**2-350**2 }{ 2 * 100 * 350 } ) = 73° 23'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 100**2-335.41**2-350**2 }{ 2 * 335.41 * 350 } ) = 16° 36'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 350**2-335.41**2-100**2 }{ 2 * 100 * 335.41 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16770.51 }{ 392.71 } = 42.71 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 335.41 }{ 2 * sin 73° 23'54" } = 175 ; ;
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