Can you help me with a physics question

A steel (Young's modulus 2.0 x 1011 N/m2) wire is strung between two supports attached to a ceiling. Initially, there is no tension in the wire when it is horizontal. A 86-N picture is then hung from the center of the wire, as the drawing illustrates, so the ends of the wire make angles of 26° with respect to the horizontal. What is the radius of the wire?

It almost looks like there is not enough information, but with a little imagination, we can supply the numbers we need.

Formula
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Y = F * L/(dL * Area)

Suppose that the wire is initially 2L units long. That means that the wire will stretch to a length of 2 times the hypotenuse of the triangle - 2L.

Find the length of the hypotenuse
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cos(26) = L / hypotenuse
hypotenuse = L/cos(26) = 1.1126 L

Next
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Find the change in length
1.1126 L - L = 0.1126L

The total change in length is twice this amount because the hypotenuse is 1/2 the total length of the wire.

L/dL = 2L/2*0.1126L = 8.881

Sin(26)*T + Sin(26)*T = 86N This is the vertical component of the tension. The horizontal components cancel out. 2*sin(26)*t = 86
T = 98.09 N

F = 98.09N
A = ???
Y = 2*10^11 N/m^2
L/dL = 8.881

A = 98.09*8.881/2*10^11
A = 4.3557 * 10^-9

pi*r^2 = 4.357 * 10^-9
r^2 = 1.386 * 10^-9
r = 3.7325 * 10^-5 m
r = 3.7325*10^-2 mm which is not very much.