# 90.5 106 135 triangle

### Acute scalene triangle.

Sides: a = 90.5   b = 106   c = 135

Area: T = 4787.089937167
Perimeter: p = 331.5
Semiperimeter: s = 165.75

Angle ∠ A = α = 41.9944180209° = 41°59'39″ = 0.73329367113 rad
Angle ∠ B = β = 51.59554998995° = 51°35'44″ = 0.90105113525 rad
Angle ∠ C = γ = 86.41103198915° = 86°24'37″ = 1.50881445898 rad

Height: ha = 105.7922030313
Height: hb = 90.32224409749
Height: hc = 70.92198425432

Median: ma = 112.619854865
Median: mb = 101.9743648557
Median: mc = 71.81113848913

Inradius: r = 28.88113838411
Circumradius: R = 67.63326938695

Vertex coordinates: A[135; 0] B[0; 0] C[56.21994444444; 70.92198425432]
Centroid: CG[63.74398148148; 23.64399475144]
Coordinates of the circumscribed circle: U[67.5; 4.23545342182]
Coordinates of the inscribed circle: I[59.75; 28.88113838411]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.0065819791° = 138°21″ = 0.73329367113 rad
∠ B' = β' = 128.4054500101° = 128°24'16″ = 0.90105113525 rad
∠ C' = γ' = 93.59896801085° = 93°35'23″ = 1.50881445898 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 ### 6. Inradius ### 7. Circumradius ### 8. Calculation of medians #### Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.