anonymous
  • anonymous
There is a bamboo 14ft high in which, while still attached, the upper end breaks and the top falls to the ground 6ft from the stem. Set up and solve an equation that can be used to find the exact height of the break and exactly how much broke off. Also, use trig to find to find the angle that the broken part makes with the ground.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Okay a drawing would help: you have the bamboo separated by upper part and lower part:|dw:1378574026740:dw|
anonymous
  • anonymous
|dw:1378574054214:dw|
anonymous
  • anonymous
When it falls, it forms this triangle as Card Mich showed.

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anonymous
  • anonymous
So you have:|dw:1378574141114:dw| We can compute many things
anonymous
  • anonymous
6^2+x^2=14-x^2
anonymous
  • anonymous
The we know that: \[6^2+x^2=(14-x)^2\] And can simplify this to: \[\eqalign{ &36+x^2=196-28x+x^2 \\ &28x=196-36 \\ &28x=160 \\ &x=\frac{160}{28}=\frac{40}{7}\\ }\]
anonymous
  • anonymous
Therefore, \(14-\frac{40}{7}=\frac{58}{7}\) Is the length that broke off. We can find the angle too:
anonymous
  • anonymous
\[\eqalign{ &tan(\theta)=\frac{x}{6} \\ &tan(\theta)=\frac{40/7}{6} \\ &tan(\theta)=\frac{40}{42} \\ &tan(\theta)=\frac{20}{21} \\ &\theta=tan^{-1}\left(\frac{20}{21}\right)\approx43.6^\circ }\]

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