Image of the triangle There is a right triangle DEF with the adjacent is 12 and the acute angle of D being 25 degrees and E being the right angle... I have to figure out angle F, DF, and DE... I'm honestly not sure on what to do and i'm stressing out.. I may have worded this wrong or missed something but any help would be appreciated, thank you so much.
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Angle $F$. Remember, the insides of a triangle add up to $180$ degrees.
Length of $DF$. Remember, $\sin \theta=\frac{opp}{hyp}=\frac{12}{DF}$
So we have $\sin 25=\frac{12}{DF}$. You can solve from here.
Length of $DE$. After you calculate angle $F$, then we know $\tan\theta=\frac{opp}{adj}=\frac{DE}{9}$
So we have $\tan \text{ (angle F)}=\frac{DE}{9}$. You can solve from here.
K Split X
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I'm not being lazy, but i'm honestly having a hard time understanding this whole section. How do i figure out the sin 25= 12/DF? It makes no sense to me and i'm feeling stupid here. Also, the same with the length of DE. I just don't get any of this and its frustrating – danneh Feb 06 '17 at 20:19
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sin $25$ you just evaluate in your calculator. We basically have $\sin(25) = \frac{12}{DF}$, and so solving for $DF$, we see that $DF=\frac{12}{\sin(25)} = 28.4$ – K Split X Feb 06 '17 at 20:35
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If you don't understand your textbook, I highly recommend khanacademy. – K Split X Feb 06 '17 at 20:36
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Either your teacher wants you to leave it in ratio form, in which case you say $DF=\frac{12}{\sin(25)}$, or it's impossible to calculate cause its too precise. Your question says $round$, so you gotta use the calc – K Split X Feb 06 '17 at 20:47