Question

Day 6: Textbook Page 321 Problem 9 When Esteban looks at the puddle, he sees a reflection of the top of the cactus. How tall is the cactus? use 10 m, 2.5 m, 1.5 m

Answer 1

The given figure can be drawn as,

From the figure,

`\tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}`

`\begin{gathered} \tan \theta=(DE)/(EC) \\ \tan \theta=(1.5)/(2.5) \\ \tan \theta=0.6 \end{gathered}`

Since angle of incidence will be equal to angle of reflection,
`\begin{gathered} \text{tan}<\text{ACB}=\frac{h}{10\text{ m}} \\ \text{tan}\theta=\frac{h}{10\text{ m}} \\ 0.6=\frac{h}{10\text{ m}} \\ 6\text{ m=h} \end{gathered}`Therefore, the height of cactus is 6 m.