Chapter 7.5, Problem 2CYP

To determine

To find: The distance between Liliana’s thumb and clock.

Answer to Problem 2CYP

900 cm

Explanation of Solution

Given:Clock is 30 cm wide.

Clock appears to move 3 clock widths when eyes are switched.

Arm is about 10 times longer than the distance between eyes.

Kindly refer to the diagram below.

  

Let the wall be towards $DF$ where the clock is situated.

  $\Delta ACB\sim \Delta DCF$

Ratio between altitude $\overline{QC}$ of $\Delta ACB$ and side $AB$ is $\frac{10}{1}$ .

Let

  $\begin{array}{l}AB=1\\ \Rightarrow QC=10\end{array}$

Let the altitude $\overline{CP}$ of $\Delta DCF$ be $x$ .

  $DF=3\times 30=90$ cm

Altitudes of two similar triangles are proportional to corresponding sides of the similar triangles.

  $\begin{array}{l}\frac{PC}{QC}=\frac{AB}{\text{}DF}\\ \Rightarrow \frac{10}{x}=\frac{1}{\text{}90}\\ \Rightarrow x=900\text{cm}\end{array}$