Right triangle calculator (a,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 a and hypotenuse c.

Right scalene triangle.

Sides: a = 77   b = 36   c = 85

Area: T = 1386
Perimeter: p = 198
Semiperimeter: s = 99

Angle ∠ A = α = 64.94223845817° = 64°56'33″ = 1.1333458435 rad
Angle ∠ B = β = 25.05876154183° = 25°3'27″ = 0.43773378917 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 36
Height: hb = 77
Height: hc = 32.61217647059

Median: ma = 52.70991073724
Median: mb = 79.07659128939
Median: mc = 42.5

Inradius: r = 14
Circumradius: R = 42.5

Vertex coordinates: A[85; 0] B[0; 0] C[69.75329411765; 32.61217647059]
Centroid: CG[51.58443137255; 10.87105882353]
Coordinates of the circumscribed circle: U[42.5; 0]
Coordinates of the inscribed circle: I[63; 14]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 115.0587615418° = 115°3'27″ = 1.1333458435 rad
∠ B' = β' = 154.9422384582° = 154°56'33″ = 0.43773378917 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus a and hypotenuse c

a = 77 ; ; c = 85 ; ;

2. 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{ 85**2 - 77**2 } = 36 ; ;
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 = 77 ; ; b = 36 ; ; c = 85 ; ;

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

p = a+b+c = 77+36+85 = 198 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 198 }{ 2 } = 99 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 77 * 36 }{ 2 } = 1386 ; ;

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

h _a = b = 36 ; ; h _b = a = 77 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1386 }{ 85 } = 32.61 ; ;

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{ 77 }{ 85 } ) = 64° 56'33" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 36 }{ 85 } ) = 25° 3'27" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1386 }{ 99 } = 14 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 77 }{ 2 * sin 64° 56'33" } = 42.5 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 36**2+2 * 85**2 - 77**2 } }{ 2 } = 52.709 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 85**2+2 * 77**2 - 36**2 } }{ 2 } = 79.076 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 36**2+2 * 77**2 - 85**2 } }{ 2 } = 42.5 ; ;
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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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