Right triangle calculator (a,b) - result

Please enter two properties of the right triangle

Use symbols: a, b, c, A, B, h, T, p, r, R


You have entered median ma and median mb.

Right scalene triangle.

Sides: a = 6   b = 20.78546096908   c = 21.63333076528

Area: T = 62.35438290725
Perimeter: p = 48.41879173436
Semiperimeter: s = 24.20989586718

Angle ∠ A = α = 16.1022113752° = 16°6'8″ = 0.28110349015 rad
Angle ∠ B = β = 73.8987886248° = 73°53'52″ = 1.29897614253 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 20.78546096908
Height: hb = 6
Height: hc = 5.7654613537

Median: ma = 21
Median: mb = 12
Median: mc = 10.81766538264

Inradius: r = 2.5765651019
Circumradius: R = 10.81766538264

Vertex coordinates: A[21.63333076528; 0] B[0; 0] C[1.66441005887; 5.7654613537]
Centroid: CG[7.76658027472; 1.92215378457]
Coordinates of the circumscribed circle: U[10.81766538264; -0]
Coordinates of the inscribed circle: I[3.4244348981; 2.5765651019]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.8987886248° = 163°53'52″ = 0.28110349015 rad
∠ B' = β' = 106.1022113752° = 106°6'8″ = 1.29897614253 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: median ma and median mb

ma = 21 ; ; mb = 12 ; ;

2. From we calculate hypotenuse c - Pythagorean theorem:

c**2 = a**2+b**2 ; ; c = sqrt{ a**2+b**2 } = sqrt{ 6**2 + 20.785**2 } = 21.633 ; ;
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 = 6 ; ; b = 20.78 ; ; c = 21.63 ; ;

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

p = a+b+c = 6+20.78+21.63 = 48.42 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48.42 }{ 2 } = 24.21 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 6 * 20.78 }{ 2 } = 62.35 ; ;

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

h _a = b = 20.78 ; ; h _b = a = 6 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 62.35 }{ 21.63 } = 5.76 ; ;

7. 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{ 6 }{ 21.63 } ) = 16° 6'8" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 20.78 }{ 21.63 } ) = 73° 53'52" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 62.35 }{ 24.21 } = 2.58 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 16° 6'8" } = 10.82 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 20.78**2+2 * 21.63**2 - 6**2 } }{ 2 } = 21 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 21.63**2+2 * 6**2 - 20.78**2 } }{ 2 } = 12 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 20.78**2+2 * 6**2 - 21.63**2 } }{ 2 } = 10.817 ; ;
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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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