# Isosceles triangle calculator (h)

Please enter two properties of the isosceles triangle

Use symbols: a, b, h, T, p, A, B, C, r, R

You have entered height hc and angle γ.

### Acute isosceles triangle.

Sides: a = 31.94546410072   b = 31.94546410072   c = 24.44993697326

Area: T = 360.787712446
Perimeter: p = 88.33986517471
Semiperimeter: s = 44.16993258735

Angle ∠ A = α = 67.5° = 67°30' = 1.17880972451 rad
Angle ∠ B = β = 67.5° = 67°30' = 1.17880972451 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 22.58882722788
Height: hb = 22.58882722788
Height: hc = 29.513

Median: ma = 23.53772229125
Median: mb = 23.53772229125
Median: mc = 29.513

Inradius: r = 8.1688273283
Circumradius: R = 17.28883151337

Vertex coordinates: A[24.44993697326; 0] B[0; 0] C[12.22546848663; 29.513]
Centroid: CG[12.22546848663; 9.83876666667]
Coordinates of the circumscribed circle: U[12.22546848663; 12.22546848663]
Coordinates of the inscribed circle: I[12.22546848663; 8.1688273283]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.5° = 112°30' = 1.17880972451 rad
∠ B' = β' = 112.5° = 112°30' = 1.17880972451 rad
∠ C' = γ' = 135° = 0.78553981634 rad

# How did we calculate this triangle?

### 1. Input data entered: angle γ and height hc ### 2. From we calculate side b: ### 3. From height h we calculate side c - Pythagorean theorem: ### 4. From side c we calculate perimeter p: 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 using Heron's formula ### 8. Calculate the heights of the triangle from its area. ### 9. Calculation of the inner angles of the triangle using a Law of Cosines    