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 = 7.31877865506   b = 1.1   c = 7.4

Area: T = 4.02547826028
Perimeter: p = 15.81877865506
Semiperimeter: s = 7.90988932753

Angle ∠ A = α = 81.45113781075° = 81°27'5″ = 1.42215947283 rad
Angle ∠ B = β = 8.54986218925° = 8°32'55″ = 0.14992015985 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 1.1
Height: hb = 7.31877865506
Height: hc = 1.08877790818

Median: ma = 3.8210667481
Median: mb = 7.33884262618
Median: mc = 3.7

Inradius: r = 0.50988932753
Circumradius: R = 3.7

Vertex coordinates: A[7.4; 0] B[0; 0] C[7.23664864865; 1.08877790818]
Centroid: CG[4.87988288288; 0.36325930273]
Coordinates of the circumscribed circle: U[3.7; 0]
Coordinates of the inscribed circle: I[6.80988932753; 0.50988932753]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 98.54986218925° = 98°32'55″ = 1.42215947283 rad
∠ B' = β' = 171.4511378107° = 171°27'5″ = 0.14992015985 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 = 1.1 ; ; c = 7.4 ; ;

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{ 7.4**2 - 1.1**2 } = 7.318 ; ;


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 = 7.32 ; ; b = 1.1 ; ; c = 7.4 ; ;

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

p = a+b+c = 7.32+1.1+7.4 = 15.82 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.82 }{ 2 } = 7.91 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.91 * (7.91-7.32)(7.91-1.1)(7.91-7.4) } ; ; T = sqrt{ 16.2 } = 4.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.02 }{ 7.32 } = 1.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.02 }{ 1.1 } = 7.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.02 }{ 7.4 } = 1.09 ; ;

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{ 7.32**2-1.1**2-7.4**2 }{ 2 * 1.1 * 7.4 } ) = 81° 27'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.1**2-7.32**2-7.4**2 }{ 2 * 7.32 * 7.4 } ) = 8° 32'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.4**2-7.32**2-1.1**2 }{ 2 * 1.1 * 7.32 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.02 }{ 7.91 } = 0.51 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.32 }{ 2 * sin 81° 27'5" } = 3.7 ; ;
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