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 = 710   b = 572   c = 911.7487772139

Area: T = 203060
Perimeter: p = 2193.748777214
Semiperimeter: s = 1096.874388607

Angle ∠ A = α = 51.14439068697° = 51°8'38″ = 0.89326295672 rad
Angle ∠ B = β = 38.85660931303° = 38°51'22″ = 0.67881667596 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 572
Height: hb = 710
Height: hc = 445.4330208233

Median: ma = 673.2087991634
Median: mb = 765.4388436453
Median: mc = 455.8743886069

Inradius: r = 185.1266113931
Circumradius: R = 455.8743886069

Vertex coordinates: A[911.7487772139; 0] B[0; 0] C[552.894413959; 445.4330208233]
Centroid: CG[488.2143970576; 148.4776736078]
Coordinates of the circumscribed circle: U[455.8743886069; 0]
Coordinates of the inscribed circle: I[524.8743886069; 185.1266113931]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.856609313° = 128°51'22″ = 0.89326295672 rad
∠ B' = β' = 141.144390687° = 141°8'38″ = 0.67881667596 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 = 710 ; ; b = 572 ; ;

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{ 710**2 + 572**2 } = 911.748 ; ;


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 = 710 ; ; b = 572 ; ; c = 911.75 ; ;

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

p = a+b+c = 710+572+911.75 = 2193.75 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2193.75 }{ 2 } = 1096.87 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1096.87 * (1096.87-710)(1096.87-572)(1096.87-911.75) } ; ; T = sqrt{ 41233363600 } = 203060 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 203060 }{ 710 } = 572 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 203060 }{ 572 } = 710 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 203060 }{ 911.75 } = 445.43 ; ;

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{ 710**2-572**2-911.75**2 }{ 2 * 572 * 911.75 } ) = 51° 8'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 572**2-710**2-911.75**2 }{ 2 * 710 * 911.75 } ) = 38° 51'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 911.75**2-710**2-572**2 }{ 2 * 572 * 710 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 203060 }{ 1096.87 } = 185.13 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 710 }{ 2 * sin 51° 8'38" } = 455.87 ; ;
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