# Right triangle calculator (A,a)

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 angle α.

### Right scalene triangle.

Sides: a = 591   b = 1933.074389752   c = 2021.399943932

Area: T = 571223.3376718
Perimeter: p = 4545.473333685
Semiperimeter: s = 2272.737666842

Angle ∠ A = α = 17° = 0.29767059728 rad
Angle ∠ B = β = 73° = 1.2744090354 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 1933.074389752
Height: hb = 591
Height: hc = 565.1766110774

Median: ma = 1955.52993256
Median: mb = 1132.905541235
Median: mc = 1010.769971966

Inradius: r = 251.3377229101
Circumradius: R = 1010.769971966

Vertex coordinates: A[2021.399943932; 0] B[0; 0] C[172.7921677491; 565.1766110774]
Centroid: CG[731.3977038938; 188.3922036925]
Coordinates of the circumscribed circle: U[1010.769971966; -0]
Coordinates of the inscribed circle: I[339.6632770899; 251.3377229101]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163° = 0.29767059728 rad
∠ B' = β' = 107° = 1.2744090354 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# How did we calculate this triangle?

### 1. Input data entered: cathetus a and angle α ### 2. From angle α we calculate angle β: ### 3. From cathetus a and angle α we calculate hypotenuse c: ### 4. From cathetus a and hypotenuse c we calculate cathetus b - Pythagorean theorem: 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. ### 5. The triangle circumference is the sum of the lengths of its three sides ### 6. Semiperimeter of the triangle ### 7. The triangle area - from two legs ### 8. Calculate the heights of the triangle from its area. ### 9. Calculation of the inner angles of the triangle - basic use of sine function ### 10. Inradius ### 11. Circumradius ### 12. Calculation of medians 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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