Question

m/cour16121/quizzes/2919544/take22A totem pole casts a shadow 45 feet long at the same time that a 6-foot-tallmancasts a shadow that is 3 feet long. Find the height of the totem pole.Height of the totemfeetHint: set a proportion like this oneshadow totemshadow manactual height totem actual height manucation

Answer 1

The totem pole with its shadow form a right triangle, and the same happens with the man and its shadow. Since it happens at the same time of the day, the "inclination" of the sunlight is the same for both, and those two triangles are similar, which means that their corresponding ratiso betweens sides are the same.

Using the hint given on the problem, we can estabilish the following equation for the height of the totem(let's call it h).

$\frac{45}{h}=\frac{3}{6}$

Now, we just need to solve for h.

$\begin{gathered} \frac{45}{h}=\frac{3}{6} \\ \frac{45}{h}=\frac{1}{2} \\ \frac{h}{45}=2 \\ h=2\cdot45 \\ h=90 \end{gathered}$

The height of the totem pole is 90 ft.