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In right triangle DEF, we have angle D = 25 degrees, angle E = 90 degrees, and DE = 9.  Find EF to the nearest tenth. You may use a calculator for this problem.

 Jun 18, 2022
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Using a CPhill diagram, we have: 

 

D

  \(25^ \circ\)

 

9

 

   \(90^ \circ\)

E                       F

 

Recalling sah cah toa, we realize the only way to find side \(EF\) is by using either tan or cos. But, notice that cos uses the hypotenuse, which we don't know. This means that we have to use tan. 

 

So, taking the tan of \(\angle D\), we have: \(\tan(25) = {EF \over 9} \), meaning \(EF = 9 \times \tan(25) \approx \color{brown}\boxed{4.2}\)

 Jun 19, 2022

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