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 = 7.48879903846   b = 1.3   c = 7.6

Area: T = 4.867719375
Perimeter: p = 16.38879903846
Semiperimeter: s = 8.19439951923

Angle ∠ A = α = 80.15109730894° = 80°9'3″ = 1.39988983791 rad
Angle ∠ B = β = 9.84990269107° = 9°50'57″ = 0.17218979477 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 1.3
Height: hb = 7.48879903846
Height: hc = 1.28108404605

Median: ma = 3.96332688529
Median: mb = 7.51661492801
Median: mc = 3.8

Inradius: r = 0.59439951923
Circumradius: R = 3.8

Vertex coordinates: A[7.6; 0] B[0; 0] C[7.37876315789; 1.28108404605]
Centroid: CG[4.99325438596; 0.42769468202]
Coordinates of the circumscribed circle: U[3.8; 0]
Coordinates of the inscribed circle: I[6.89439951923; 0.59439951923]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 99.84990269106° = 99°50'57″ = 1.39988983791 rad
∠ B' = β' = 170.1510973089° = 170°9'3″ = 0.17218979477 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 = 1.3 ; ; c = 7.6 ; ;

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{ 7.6**2 - 1.3**2 } = 7.488 ; ;


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 = 7.49 ; ; b = 1.3 ; ; c = 7.6 ; ;

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

p = a+b+c = 7.49+1.3+7.6 = 16.39 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.39 }{ 2 } = 8.19 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.19 * (8.19-7.49)(8.19-1.3)(8.19-7.6) } ; ; T = sqrt{ 23.69 } = 4.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.87 }{ 7.49 } = 1.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.87 }{ 1.3 } = 7.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.87 }{ 7.6 } = 1.28 ; ;

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{ 7.49**2-1.3**2-7.6**2 }{ 2 * 1.3 * 7.6 } ) = 80° 9'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.3**2-7.49**2-7.6**2 }{ 2 * 7.49 * 7.6 } ) = 9° 50'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.6**2-7.49**2-1.3**2 }{ 2 * 1.3 * 7.49 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.87 }{ 8.19 } = 0.59 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.49 }{ 2 * sin 80° 9'3" } = 3.8 ; ;
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