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 Pythagorean triangle.

Sides: a = 45   b = 60   c = 75

Area: T = 1350
Perimeter: p = 180
Semiperimeter: s = 90

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 = 60
Height: hb = 45
Height: hc = 36

Median: ma = 64.08800280899
Median: mb = 54.0833269132
Median: mc = 37.5

Inradius: r = 15
Circumradius: R = 37.5

Vertex coordinates: A[75; 0] B[0; 0] C[27; 36]
Centroid: CG[34; 12]
Coordinates of the circumscribed circle: U[37.5; 0]
Coordinates of the inscribed circle: I[30; 15]

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

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: cathetus a and hypotenuse c

a = 45 ; ; c = 75 ; ;

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{ 75**2 - 45**2 } = 60 ; ;


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 = 45 ; ; b = 60 ; ; c = 75 ; ;

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

p = a+b+c = 45+60+75 = 180 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 180 }{ 2 } = 90 ; ;

5. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 45 * 60 }{ 2 } = 1350 ; ;

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

h _a = b = 60 ; ; h _b = a = 45 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1350 }{ 75 } = 36 ; ;

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{ 45 }{ 75 } ) = 36° 52'12" ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 60 }{ 75 } ) = 53° 7'48" ; ; gamma = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1350 }{ 90 } = 15 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 45 }{ 2 * sin 36° 52'12" } = 37.5 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 75**2 - 45**2 } }{ 2 } = 64.08 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 75**2+2 * 45**2 - 60**2 } }{ 2 } = 54.083 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 45**2 - 75**2 } }{ 2 } = 37.5 ; ;
Calculate another triangle

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.

Calculate right triangle by:

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.