#1**0 **

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.

Guest Mar 5, 2023