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
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The given figure can be drawn as,
From the figure,
[tex]\tan \theta=\frac{opposite\text{ side}}{\text{adjacent side}}[/tex][tex]\begin{gathered} \tan \theta=\frac{DE}{EC} \\ \tan \theta=\frac{1.5}{2.5} \\ \tan \theta=0.6 \end{gathered}[/tex]Since angle of incidence will be equal to angle of reflection, [tex]\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}[/tex]Therefore, the height of cactus is 6 m.