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 = 157999.9221997   b = 157   c = 158000

Area: T = 12402993.87768
Perimeter: p = 316156.9221997
Semiperimeter: s = 158078.4610998

Angle ∠ A = α = 89.94330668426° = 89°56'35″ = 1.57698026557 rad
Angle ∠ B = β = 0.05769331574° = 0°3'25″ = 0.0010993671 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 157
Height: hb = 157999.9221997
Height: hc = 1576.999922491

Median: ma = 79000.11770047
Median: mb = 157999.9411498
Median: mc = 79000

Inradius: r = 78.46109984081
Circumradius: R = 79000

Vertex coordinates: A[158000; 0] B[0; 0] C[157999.8443994; 1576.999922503]
Centroid: CG[105333.2811331; 52.33333075011]
Coordinates of the circumscribed circle: U[79000; 0]
Coordinates of the inscribed circle: I[157921.4610998; 78.46109984145]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.05769331574° = 90°3'25″ = 1.57698026557 rad
∠ B' = β' = 179.9433066843° = 179°56'35″ = 0.0010993671 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus b hypotenuse c

b = 157 ; ; c = 158000 ; ;

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

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 158000**2 - 157**2 } = 157999.922 ; ;


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 = 157999.92 ; ; b = 157 ; ; c = 158000 ; ;

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

p = a+b+c = 157999.92+157+158000 = 316156.92 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 316156.92 }{ 2 } = 158078.46 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 158078.46 * (158078.46-157999.92)(158078.46-157)(158078.46-158000) } ; ; T = sqrt{ 1.538 * 10**{ 14 } } = 12402993.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12402993.88 }{ 157999.92 } = 157 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12402993.88 }{ 157 } = 157999.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12402993.88 }{ 158000 } = 157 ; ;

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{ 157999.92**2-157**2-158000**2 }{ 2 * 157 * 158000 } ) = 89° 56'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 157**2-157999.92**2-158000**2 }{ 2 * 157999.92 * 158000 } ) = 0° 3'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 158000**2-157999.92**2-157**2 }{ 2 * 157 * 157999.92 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12402993.88 }{ 158078.46 } = 78.46 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 157999.92 }{ 2 * sin 89° 56'35" } = 79000 ; ;
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