College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.9 - Modeling with Equations - P.9 Exercises: 46

Answer

95 feet

Work Step by Step

Let's say that $x$ is the height of the tall tree. We can find two similar triangles by starting at the eye level of the woodcutter. We set up a ratio between the large triangle and the small triangle: $\frac{x-5}{25+125}=\frac{20-5}{25}$ We cross multiply to solve for $x$: $(x-5)*25=(20-5)*(25+125)$ $25*x-125=15*150$ $25*x-125=2250$ $25*x=2375$ $x=95$ Thus the height of the tall tree is 95 feet.
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