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 hypotenuse c, angle α and angle γ.

Right scalene triangle.

Sides: a = 95.45994154602   b = 95.45994154602   c = 135

Area: T = 4556.25
Perimeter: p = 325.919883092
Semiperimeter: s = 162.959941546

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 95.45994154602
Height: hb = 95.45994154602
Height: hc = 67.5

Median: ma = 106.7276871031
Median: mb = 106.7276871031
Median: mc = 67.5

Inradius: r = 27.95994154602
Circumradius: R = 67.5

Vertex coordinates: A[135; 0] B[0; 0] C[67.5; 67.5]
Centroid: CG[67.5; 22.5]
Coordinates of the circumscribed circle: U[67.5; -0]
Coordinates of the inscribed circle: I[67.5; 27.95994154602]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

1. Input data entered: hypotenuse c, angle α and angle γ

c = 135 ; ; alpha = 45° ; ; gamma = 90° ; ;

2. From angle α we calculate angle β:

alpha + beta + 90° = 180° ; ; beta = 90° - alpha = 90° - 45 ° = 45 ° ; ;

3. From hypotenuse c and angle α we calculate cathetus a:

sin alpha = a:c ; ; a = c * sin alpha = 135 * sin(45 ° ) = 95.459 ; ;

4. 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{ 135**2 - 95.459**2 } = 95.459 ; ;
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 = 95.46 ; ; b = 95.46 ; ; c = 135 ; ;

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

p = a+b+c = 95.46+95.46+135 = 325.92 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 325.92 }{ 2 } = 162.96 ; ;

7. The triangle area - from two legs

T = fraction{ ab }{ 2 } = fraction{ 95.46 * 95.46 }{ 2 } = 4556.25 ; ;

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

h _a = b = 95.46 ; ; h _b = a = 95.46 ; ; T = fraction{ c h _c }{ 2 } ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4556.25 }{ 135 } = 67.5 ; ;

9. 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{ 95.46 }{ 135 } ) = 45° ; ; sin beta = fraction{ b }{ c } ; ; beta = arcsin( fraction{ b }{ c } ) = arcsin( fraction{ 95.46 }{ 135 } ) = 45° ; ; gamma = 90° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4556.25 }{ 162.96 } = 27.96 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 95.46 }{ 2 * sin 45° } = 67.5 ; ;

12. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 95.46**2+2 * 135**2 - 95.46**2 } }{ 2 } = 106.727 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 135**2+2 * 95.46**2 - 95.46**2 } }{ 2 } = 106.727 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 95.46**2+2 * 95.46**2 - 135**2 } }{ 2 } = 67.5 ; ;
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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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