To find the circumradius (R) of a triangle with side lengths a, b, and c, we can use the following formula:
R = (abc) / (4Δ)
where Δ is the area of the triangle.
First, we can use the Law of Cosines to find the angle opposite the side of length 40:
cos(C) = (a^2 + b^2 - c^2) / 2ab cos(C) = (29^2 + 29^2 - 40^2) / (2 * 29 * 29) cos(C) = 21 / 29
C = cos^-1(21/29) C ≈ 47.94°
Now we can use the formula for the area of a triangle:
Δ = (1/2) * ab * sin(C)
Δ = (1/2) * 29 * 29 * sin(47.94°) Δ = 400
Finally, we can use the formula for the circumradius:
R = (abc) / (4Δ)
R = (29 * 29 * 40) / (4 * 400) = 841/40
Therefore, the circumradius of the triangle is 841/40.
