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In sunlight, a vertical stick 7 ft tall casts a shadow 3 ft long. At the same time a nearby tree casts a shadow 11 ft long. How tall is the tree? Round to the nearest tenth.

Sagot :

[tex]look\ at\ the\ picture\\\\\Delta ABC\sim\Delta D EF\\\\\frac{|ED|}{|EF|}=\frac{|AB|}{|BC|}\\\\\frac{|ED|}{11}=\frac{7}{3}\ \ \ \ /\cdot11\\\\|ED|=\frac{77}{3}\\\\|ED|\approx25.7\ (ft)\leftarrow Answer[/tex]
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Answer:

25.7 feet.

Step-by-step explanation:

Let x be the actual length of tree.

We have been given that in sunlight, a vertical stick 7 ft tall casts a shadow 3 ft long. We are asked to find the actual length of tree casting a 11 ft long shadow.

We will use proportions to solve our given problem.

[tex]\frac{x}{11}=\frac{7}{3}[/tex]

Upon multiplying both sides of our equation by 11, we will get:

[tex]\frac{x}{11}*11=\frac{7}{3}*11[/tex]

[tex]x=\frac{77}{3}[/tex]

[tex]x=25.6666666\approx 25.7[/tex]

Therefore, the tree is 25.7 feet tall.

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