Question

If you hold a 28.02 cm² square plane mirror 40.26 cm from your eyes and can just see the full length of a 8.9 m flag pole behind you, how far are you from the pole?

Answer 1

ANSWER:

66.8 m

STEP-BY-STEP EXPLANATION:

Given:

Area of mirror = 28.02 cm²

We make a sketch of the situation in order to solve the problem:

We calculate the height as follows:

$\begin{gathered} h=\sqrt{28.02}=5.3\text{ cm} \\ \\ \text{ therefore:} \\ \\ AC=\frac{5.3}{2}=2.65\text{ cm } \\ \\ \text{ For ABC:} \\ \\ \tan\theta=\frac{2.65}{40.26} \end{gathered}$

Now, we determine for AEF that it has the same angle as ABC, like this:

$\begin{gathered} \tan\theta=\frac{EF}{EA}=\frac{\frac{890}{2}-2.65}{d} \\ \\ \text{ Therefore:} \\ \\ \frac{2.65}{40.26}=\frac{\frac{890}{2}-2.65}{d} \\ \\ \text{ we solve for d:} \\ \\ \:d=\frac{40.26}{2.65}\cdot\left(\frac{890}{2}-2.65\right)\: \\ \\ d=6720.38\text{ cm} \\ \\ d=67.2\text{ m} \\ \\ \text{ Therefore:} \\ \\ D=67.2-0.4026=66.7974\equiv66.8\text{ m} \end{gathered}$

It is located 66.8 meters from the pole