# 78 110 90 triangle

### Acute scalene triangle.

Sides: a = 78   b = 110   c = 90

Area: T = 3471.118783148
Perimeter: p = 278
Semiperimeter: s = 139

Angle ∠ A = α = 44.52662467768° = 44°31'34″ = 0.77771296098 rad
Angle ∠ B = β = 81.46438696679° = 81°27'50″ = 1.42218127471 rad
Angle ∠ C = γ = 54.01098835553° = 54°36″ = 0.94326502967 rad

Height: ha = 89.00330213199
Height: hb = 63.11112332996
Height: hc = 77.13659518106

Median: ma = 92.6232891339
Median: mb = 63.7733035054
Median: mc = 84.06554506917

Inradius: r = 24.97220707301
Circumradius: R = 55.61660895056

Vertex coordinates: A[90; 0] B[0; 0] C[11.57877777778; 77.13659518106]
Centroid: CG[33.85992592593; 25.71219839369]
Coordinates of the circumscribed circle: U[45; 32.68325551617]
Coordinates of the inscribed circle: I[29; 24.97220707301]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.4743753223° = 135°28'26″ = 0.77771296098 rad
∠ B' = β' = 98.53661303321° = 98°32'10″ = 1.42218127471 rad
∠ C' = γ' = 125.9990116445° = 125°59'24″ = 0.94326502967 rad

# How did we calculate this triangle?

### 1. The triangle circumference is the sum of the lengths of its three sides ### 2. Semiperimeter of the triangle ### 3. The triangle area using Heron's formula ### 4. Calculate the heights of the triangle from its area. ### 5. Calculation of the inner angles of the triangle using a Law of Cosines    