A tree with a height of 12 yards casts a shadow that is 33 yards long at a certain time of day. At the same time, another tree nearby casts a shadow that is 20 yards long. How tall is the second tree?

Answer: Height of second tree would be 7.27 yards.Step-by-step explanation:Since we have given thatHeight of a tree = 12 yardsLength of shadow of tree = 33 yardsIf the shadow of tree = 20 yardsThen, we need to find the height of tree.Since there is direct relation between height of tree and length of its shadow.So, Let the height of tree in the second case be 'x'.So, it becomes, [tex]\dfrac{12}{33}=\dfrac{x}{20}\\\\\dfrac{12\times 20}{33}=x\\\\7.27\ yards=x[/tex]Hence, height of second tree would be 7.27 yards.

[tex]Shadow\ of\ second\ three\ is\\\\
33+20=53\\
Triangles\ made\ of\ three\ and\ shadows\ are\ similar, so\\
Proportion\ of\ length\ of\ shadow:\ \frac{53}{33}\\\\
Height\ will\ be\ on\ the\ same\ proportion\\\\
\frac{x}{12}=\frac{53}{33}\\\\
3x=53*12\\
3x=636\\
x=212\\
Second\ three\ has\ 212\ yards.[/tex]