# 1523 411.5 1540 triangle

### Acute scalene triangle.

Sides: a = 1523   b = 411.5   c = 1540

Area: T = 311982.978803
Perimeter: p = 3474.5
Semiperimeter: s = 1737.25

Angle ∠ A = α = 79.93994893515° = 79°56'22″ = 1.39552072915 rad
Angle ∠ B = β = 15.42985161254° = 15°25'43″ = 0.26992784051 rad
Angle ∠ C = γ = 84.63219945231° = 84°37'55″ = 1.4777106957 rad

Height: ha = 409.6955309298
Height: hb = 1516.321067086
Height: hc = 405.173269874

Median: ma = 831.0143763424
Median: mb = 1517.644008826
Median: mc = 807.1744469988

Vertex coordinates: A[1540; 0] B[0; 0] C[1468.116582792; 405.173269874]
Centroid: CG[1002.705527597; 135.0587566247]
Coordinates of the circumscribed circle: U[770; 72.35326352865]
Coordinates of the inscribed circle: I[1325.75; 179.5844387987]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 100.0610510649° = 100°3'38″ = 1.39552072915 rad
∠ B' = β' = 164.5711483875° = 164°34'17″ = 0.26992784051 rad
∠ C' = γ' = 95.36880054769° = 95°22'5″ = 1.4777106957 rad

# How did we calculate this triangle?

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. ### 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    