Right triangle calculator (a,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 a and hypotenuse c.

Right scalene triangle.

Sides: a = 37   b = 87.49985714169   c = 95

Area: T = 1618.724357121
Perimeter: p = 219.4998571417
Semiperimeter: s = 109.7499285708

Angle ∠ A = α = 22.92217544629° = 22°55'18″ = 0.44000600857 rad
Angle ∠ B = β = 67.07882455371° = 67°4'42″ = 1.17107362411 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 87.49985714169
Height: hb = 37
Height: hc = 34.07883909729

Median: ma = 89.43329357675
Median: mb = 57.29774694031
Median: mc = 47.5

Inradius: r = 14.74992857085
Circumradius: R = 47.5

Vertex coordinates: A[95; 0] B[0; 0] C[14.41105263158; 34.07883909729]
Centroid: CG[36.47701754386; 11.35994636576]
Coordinates of the circumscribed circle: U[47.5; -0]
Coordinates of the inscribed circle: I[22.25107142915; 14.74992857085]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.0788245537° = 157°4'42″ = 0.44000600857 rad
∠ B' = β' = 112.9221754463° = 112°55'18″ = 1.17107362411 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a hypotenuse c

a = 37 ; ; c = 95 ; ;

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

c**2 = a**2+b**2 ; ; b = sqrt{ c**2 - a**2 } = sqrt{ 95**2 - 37**2 } = 87.499 ; ;


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 = 37 ; ; b = 87.5 ; ; c = 95 ; ;

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

p = a+b+c = 37+87.5+95 = 219.5 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 219.5 }{ 2 } = 109.75 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 109.75 * (109.75-37)(109.75-87.5)(109.75-95) } ; ; T = sqrt{ 2620266 } = 1618.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1618.72 }{ 37 } = 87.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1618.72 }{ 87.5 } = 37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1618.72 }{ 95 } = 34.08 ; ;

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{ 37**2-87.5**2-95**2 }{ 2 * 87.5 * 95 } ) = 22° 55'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 87.5**2-37**2-95**2 }{ 2 * 37 * 95 } ) = 67° 4'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 95**2-37**2-87.5**2 }{ 2 * 87.5 * 37 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1618.72 }{ 109.75 } = 14.75 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 37 }{ 2 * sin 22° 55'18" } = 47.5 ; ;
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