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# trig problem

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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

#1
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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