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 = 76   b = 57   c = 95

Area: T = 2166
Perimeter: p = 228
Semiperimeter: s = 114

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

Height: ha = 57
Height: hb = 76
Height: hc = 45.6

Median: ma = 68.50554742338
Median: mb = 81.16880355805
Median: mc = 47.5

Inradius: r = 19
Circumradius: R = 47.5

Vertex coordinates: A[95; 0] B[0; 0] C[60.8; 45.6]
Centroid: CG[51.93333333333; 15.2]
Coordinates of the circumscribed circle: U[47.5; -0]
Coordinates of the inscribed circle: I[57; 19]

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

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: cathetus a hypotenuse c

a = 76 ; ; c = 95 ; ;

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{ 95**2 - 76**2 } = 57 ; ;


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 = 76 ; ; b = 57 ; ; c = 95 ; ;

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

p = a+b+c = 76+57+95 = 228 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 228 }{ 2 } = 114 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 114 * (114-76)(114-57)(114-95) } ; ; T = sqrt{ 4691556 } = 2166 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2166 }{ 76 } = 57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2166 }{ 57 } = 76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2166 }{ 95 } = 45.6 ; ;

7. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 76**2-57**2-95**2 }{ 2 * 57 * 95 } ) = 53° 7'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 57**2-76**2-95**2 }{ 2 * 76 * 95 } ) = 36° 52'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 95**2-76**2-57**2 }{ 2 * 57 * 76 } ) = 90° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2166 }{ 114 } = 19 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 76 }{ 2 * sin 53° 7'48" } = 47.5 ; ;
Trigonometry right triangle solver. Find the hypotenuse c of a triangle - calculator. Area T of right triangle calculator.

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.