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 = 55   b = 48   c = 73

Area: T = 1320
Perimeter: p = 176
Semiperimeter: s = 88

Angle ∠ A = α = 48.88879095608° = 48°53'16″ = 0.85332549863 rad
Angle ∠ B = β = 41.11220904392° = 41°6'44″ = 0.71875413405 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 48
Height: hb = 55
Height: hc = 36.16443835616

Median: ma = 55.32195263899
Median: mb = 60.00883327547
Median: mc = 36.5

Inradius: r = 15
Circumradius: R = 36.5

Vertex coordinates: A[73; 0] B[0; 0] C[41.43883561644; 36.16443835616]
Centroid: CG[38.14661187215; 12.05547945205]
Coordinates of the circumscribed circle: U[36.5; 0]
Coordinates of the inscribed circle: I[40; 15]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.1122090439° = 131°6'44″ = 0.85332549863 rad
∠ B' = β' = 138.8887909561° = 138°53'16″ = 0.71875413405 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 = 55 ; ; c = 73 ; ;

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{ 73**2 - 55**2 } = 48 ; ;


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 = 55 ; ; b = 48 ; ; c = 73 ; ;

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

p = a+b+c = 55+48+73 = 176 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 176 }{ 2 } = 88 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 55 * 48 }{ 2 } = 1320 ; ;

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

h _a = b = 48 ; ; h _b = a = 55 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1320 }{ 73 } = 36.16 ; ;

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{ 55 }{ 73 } ) = 48° 53'16" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 48 }{ 73 } ) = 41° 6'44" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1320 }{ 88 } = 15 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 55 }{ 2 * sin 48° 53'16" } = 36.5 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 48**2+2 * 73**2 - 55**2 } }{ 2 } = 55.32 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 73**2+2 * 55**2 - 48**2 } }{ 2 } = 60.008 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 48**2+2 * 55**2 - 73**2 } }{ 2 } = 36.5 ; ;
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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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