Right triangle calculator (a) - result

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 area T.

Right scalene triangle.

Sides: a = 2   b = 6   c = 6.32545553203

Area: T = 6
Perimeter: p = 14.32545553203
Semiperimeter: s = 7.16222776602

Angle ∠ A = α = 18.43549488229° = 18°26'6″ = 0.32217505544 rad
Angle ∠ B = β = 71.56550511771° = 71°33'54″ = 1.24990457724 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 6
Height: hb = 2
Height: hc = 1.89773665961

Median: ma = 6.08327625303
Median: mb = 3.60655512755
Median: mc = 3.16222776602

Inradius: r = 0.83877223398
Circumradius: R = 3.16222776602

Vertex coordinates: A[6.32545553203; 0] B[0; 0] C[0.6322455532; 1.89773665961]
Centroid: CG[2.31990036175; 0.6322455532]
Coordinates of the circumscribed circle: U[3.16222776602; -0]
Coordinates of the inscribed circle: I[1.16222776602; 0.83877223398]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.5655051177° = 161°33'54″ = 0.32217505544 rad
∠ B' = β' = 108.4354948823° = 108°26'6″ = 1.24990457724 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a and area T

a = 2 ; ; S = 6 ; ;

2. From area T and cathetus a we calculate cathetus b:

S = fraction{ ab }{ 2 } ; ; b = 2 S / a = 2 * 6/ 2 = 6 ; ;

3. 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{ 2**2 + 6**2 } = 6.325 ; ;

4. From area T and hypotenuse c we calculate height h:

S = fraction{ c * h }{ 2 } ; ; h = 2 * S / c = 2 * 6 / 6.325 = 1.897 ; ;


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 = 2 ; ; b = 6 ; ; c = 6.32 ; ;

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

p = a+b+c = 2+6+6.32 = 14.32 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 14.32 }{ 2 } = 7.16 ; ;

7. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 2 * 6 }{ 2 } = 6 ; ;

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

h _a = b = 6 ; ; h _b = a = 2 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6 }{ 6.32 } = 1.9 ; ;

9. Calculation of the inner angles of the triangle - basic use of sine function

 sin alpha = fraction{ a }{ c } ; ; alpha = arcsin( fraction{ a }{ c } ) = arcsin( fraction{ 2 }{ 6.32 } ) = 18° 26'6" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 6 }{ 6.32 } ) = 71° 33'54" ; ; gamma = 90° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6 }{ 7.16 } = 0.84 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2 }{ 2 * sin 18° 26'6" } = 3.16 ; ;

12. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 6.32**2 - 2**2 } }{ 2 } = 6.083 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 2**2 - 6**2 } }{ 2 } = 3.606 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6**2+2 * 2**2 - 6.32**2 } }{ 2 } = 3.162 ; ;
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Trigonometry right triangle solver. You can calculate angles, sides (adjacent, opposite, hypotenuse) and area of any right-angled triangle and use it in real world to find height. A right-angled triangle is entirely determined by two independent properties. Step-by-step explanations are provided for each calculation.

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