One afternoon, John, who is 5 feet 7 inches tall, casts a shadow that is 9 feet 8 inches long. At the same time of
day. a nearby tree casts a shadow that is 15 feet long John reasons he can figure out the height of the tree.
What is the height of the tree in feet? Round your answer to the nearest tenth of a foot.

Question

raniyahhgriggs2003 raniyahhgriggs2003

24-01-2020
Mathematics

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One afternoon, John, who is 5 feet 7 inches tall, casts a shadow that is 9 feet 8 inches long. At the same time of
day. a nearby tree casts a shadow that is 15 feet long John reasons he can figure out the height of the tree.
What is the height of the tree in feet? Round your answer to the nearest tenth of a foot.

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frika frika · Answer 1 · 2020-01-30T10:52:17+01:00

Answer:

8.7 feet

Step-by-step explanation:

Complete such table:

[tex]\begin{array}{ccc}&\text{Height}&\text{Shadow}\\ \\\text{John}&5\ ft\ 7\ in&9\ ft\ 8\ in\\ \\\text{Tree}&x&15\ ft\end{array}[/tex]

Convert all measures into inches:

[tex]5 \ ft\ 7 \ in=(5\cdot 12+7)\ in=67\ in\\ \\9 \ ft\ 8 \ in=(9\cdot 12+8)\ in=116\ in\\ \\15 \ ft=15\cdot 12\ in=180\ in[/tex]

Then the table will be

[tex]\begin{array}{ccc}&\text{Height}&\text{Shadow}\\ \\\text{John}&67\ in&116\ in\\ \\\text{Tree}&x&180\ in\end{array}[/tex]

Write a proportion:

[tex]\dfrac{67}{x}=\dfrac{116}{180}[/tex]

Cross multiply:

[tex]116x=180\cdot 67\\ \\116x=12,060\\ \\x=103\dfrac{28}{29}\ in[/tex]

Convert it into feet:

[tex]103\dfrac{28}{29}\ in=\left(8\cdot 12+7\dfrac{28}{29}\right)\ in=8\ ft\ 7\dfrac{28}{29}\ in\approx 8\ ft\ 8\ in=8\dfrac{8}{12}\ ft=8\dfrac{2}{3}\ ft\approx 8.7\ ft[/tex]