Right triangle calculator (A,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 hypotenuse c, angle α and angle β.

Right scalene triangle.

Sides: a = 2.25443647341   b = 4.06769816382   c = 4.65

Area: T = 4.58442299898
Perimeter: p = 10.97113463723
Semiperimeter: s = 5.48656731862

Angle ∠ A = α = 29° = 0.50661454831 rad
Angle ∠ B = β = 61° = 1.06546508437 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 4.06769816382
Height: hb = 2.25443647341
Height: hc = 1.97217118236

Median: ma = 4.22202937971
Median: mb = 3.03659916446
Median: mc = 2.325

Inradius: r = 0.83656731862
Circumradius: R = 2.325

Vertex coordinates: A[4.65; 0] B[0; 0] C[1.09329377107; 1.97217118236]
Centroid: CG[1.91443125702; 0.65772372745]
Coordinates of the circumscribed circle: U[2.325; -0]
Coordinates of the inscribed circle: I[1.4198691548; 0.83656731862]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151° = 0.50661454831 rad
∠ B' = β' = 119° = 1.06546508437 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: hypotenuse c, angle α and angle β

c = 4.65 ; ; alpha = 29° ; ; beta = 61° ; ;

2. From hypotenuse c and angle α we calculate cathetus a:

 sin alpha = a:c ; ; a = c * sin alpha = 4.65 * sin(29 ° ) = 2.254 ; ;

3. 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{ 4.65**2 - 2.254**2 } = 4.067 ; ;
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 = 2.25 ; ; b = 4.07 ; ; c = 4.65 ; ;

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

p = a+b+c = 2.25+4.07+4.65 = 10.97 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 10.97 }{ 2 } = 5.49 ; ;

6. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 2.25 * 4.07 }{ 2 } = 4.58 ; ;

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

h _a = b = 4.07 ; ; h _b = a = 2.25 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.58 }{ 4.65 } = 1.97 ; ;

8. 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{ 2.25 }{ 4.65 } ) = 29° ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 4.07 }{ 4.65 } ) = 61° ; ; gamma = 90° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.58 }{ 5.49 } = 0.84 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.25 }{ 2 * sin 29° } = 2.33 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.07**2+2 * 4.65**2 - 2.25**2 } }{ 2 } = 4.22 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.65**2+2 * 2.25**2 - 4.07**2 } }{ 2 } = 3.036 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.07**2+2 * 2.25**2 - 4.65**2 } }{ 2 } = 2.325 ; ;
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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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