Right triangle calculator

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 hypotenuse c.

Right scalene triangle.

Sides: a = 330   b = 550   c = 641.4054708433

Area: T = 90750
Perimeter: p = 1521.405470843
Semiperimeter: s = 760.7022354216

Angle ∠ A = α = 30.96437565321° = 30°57'50″ = 0.54404195003 rad
Angle ∠ B = β = 59.03662434679° = 59°2'10″ = 1.03303768265 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 550
Height: hb = 330
Height: hc = 282.9732665485

Median: ma = 574.217685799
Median: mb = 429.5643732175
Median: mc = 320.7022354216

Inradius: r = 119.2987645784
Circumradius: R = 320.7022354216

Vertex coordinates: A[641.4054708433; 0] B[0; 0] C[169.7843599291; 282.9732665485]
Centroid: CG[270.3966102575; 94.32442218284]
Coordinates of the circumscribed circle: U[320.7022354216; 0]
Coordinates of the inscribed circle: I[210.7022354216; 119.2987645784]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.0366243468° = 149°2'10″ = 0.54404195003 rad
∠ B' = β' = 120.9643756532° = 120°57'50″ = 1.03303768265 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 hypotenuse c

a = 330 ; ; b = 550 ; ; c = 641.405 ; ;


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 = 330 ; ; b = 550 ; ; c = 641.4 ; ;

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

p = a+b+c = 330+550+641.4 = 1521.4 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1521.4 }{ 2 } = 760.7 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 760.7 * (760.7-330)(760.7-550)(760.7-641.4) } ; ; T = sqrt{ 8235562500 } = 90750 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 90750 }{ 330 } = 550 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 90750 }{ 550 } = 330 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 90750 }{ 641.4 } = 282.97 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 330**2-550**2-641.4**2 }{ 2 * 550 * 641.4 } ) = 30° 57'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 550**2-330**2-641.4**2 }{ 2 * 330 * 641.4 } ) = 59° 2'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 641.4**2-330**2-550**2 }{ 2 * 550 * 330 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 90750 }{ 760.7 } = 119.3 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 330 }{ 2 * sin 30° 57'50" } = 320.7 ; ;
Trigonometry right triangle solver. Find the hypotenuse c of a triangle - calculator. Area T of right triangle calculator.

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