Chapter P, Prerequisites - Section P.9 - Modeling with Equations - P.9 Exercises - Page 71: 45

5 m

We know that the ratios between the sides of the two similar triangles will be the same (since the angles are equal). Using the image given, we have: $\displaystyle \frac{10+x}{6}=\frac{x}{2}$ We cross multiply to solve for $x$: $20+2x=6x$ $4x=20$ $x=5$ So we know that the man's shadow is 5 m long.