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 Pythagorean triangle.

Sides: a = 36.6   b = 48.8   c = 61

Area: T = 893.04
Perimeter: p = 146.4
Semiperimeter: s = 73.2

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 48.8
Height: hb = 36.6
Height: hc = 29.28

Median: ma = 52.11884228464
Median: mb = 43.98877255607
Median: mc = 30.5

Inradius: r = 12.2
Circumradius: R = 30.5

Vertex coordinates: A[61; 0] B[0; 0] C[21.96; 29.28]
Centroid: CG[27.65333333333; 9.76]
Coordinates of the circumscribed circle: U[30.5; -0]
Coordinates of the inscribed circle: I[24.4; 12.2]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: cathetus b and hypotenuse c

b = 0.75 ; ; c = 61 ; ;

2. From side b and side c we calculate side a - Pythagorean theorem:

c**2 = a**2+b**2 ; ; a = sqrt{ c**2 - b**2 } = sqrt{ 61**2 - 48.8**2 } = 36.6 ; ;


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 = 36.6 ; ; b = 48.8 ; ; c = 61 ; ;

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

p = a+b+c = 36.6+48.8+61 = 146.4 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 146.4 }{ 2 } = 73.2 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 36.6 * 48.8 }{ 2 } = 893.04 ; ;

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

h _a = b = 48.8 ; ; h _b = a = 36.6 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 893.04 }{ 61 } = 29.28 ; ;

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{ 36.6 }{ 61 } ) = 36° 52'12" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 48.8 }{ 61 } ) = 53° 7'48" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 893.04 }{ 73.2 } = 12.2 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 36.6 }{ 2 * sin 36° 52'12" } = 30.5 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 48.8**2+2 * 61**2 - 36.6**2 } }{ 2 } = 52.118 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 61**2+2 * 36.6**2 - 48.8**2 } }{ 2 } = 43.988 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 48.8**2+2 * 36.6**2 - 61**2 } }{ 2 } = 30.5 ; ;
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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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