Question

Nathan is 6 feet tall and casts a shadow 2.5 feet long. At the same time, a lamppost casts a shadow 10 feet long. Write and solve a proportion to find the height of the lamppost. Please help and explain.

Answer 1

you have many choices for ratios as the triangles are similar
you could say \[\frac{6}{2.4}=\frac{x}{10}\] or
\[\frac{x}{6}=\frac{10}{2.4}\] but the answer will be the same in any case, it will be
\[x=\frac{6\times 10}{2.4}\]