3. Four congruent right triangles can be assembled to form the square string figure shown in Figure 2(a), or the rhombus shown in Figure 2(b). If the area of the large square in Figure 2(a) is 100, and the area of the small square is 4, then the cosine value of one acute angle in the rhombus in Figure 2(b) is
3. $\frac{7}{25}$.

Let the three sides of a right-angled triangle be $a, b, c$ $(a<b<c)$, and the smallest acute angle be $\theta$. Then the acute angle of the rhombus is $2 \theta$.
According to the problem, we have
$$
\left\{\begin{array} { l } 
{ c ^ { 2 } = 1 0 0 , } \\
{ ( b - a ) ^ { 2 } = 4 , } \\
{ a ^ { 2 } + b ^ { 2 } = c ^ { 2 } }
\end{array} \Rightarrow \left\{\begin{array}{l}
a=6, \\
b=8, \\
c=10 .
\end{array}\right.\right.
$$

Therefore, $\cos \theta=\frac{8}{10}=\frac{4}{5}$.
Hence, $\cos 2 \theta=2 \cos ^{2} \theta-1=\frac{7}{25}$.