Question

How would I find the length of side EF?

http://tinypic.com/view.php?pic=2a0cgth&s=6

Answer 1

Remember SOHCAHTOA?

Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent

You know the angle, and you know Opposite. How would you find Adjacent?

Answer 2

@whpalmer4 I don't know how to do that..
all of this is really confusing to me

Answer 3

Do you know which side is the hypotenuse?

Answer 4

@whpalmer4 would that be side FD?

Answer 5

It would indeed!

Answer 6

Which side is adjacent to the angle (other than the hypotenuse)?

Answer 7

@whpalmer4 EF?

Answer 8

Right again!

Answer 9

Finally, what's the opposite, and what is its length?

Answer 10

@whpalmer4 opposite to the hypotenuse?

Answer 11

Opposite to the angle...just like EF was adjacent to the angle

Answer 12

@whpalmer4 uhmmm E?

Answer 13

No, what is the side that is opposite to the angle, and how long is it?

Answer 14

@whpalmer4 wait would the side be ED?

Answer 15

Yes, ED. And ED has a length of 14.

We know the angle, and we know the opposite. We want to know the adjacent. Which of the SOH CAH TOA entries works with that?

Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent

Looks like Tan = opposite / adjacent is what we want, because it includes the thing we want to find, and we know the remaining quantities.

\[\tan(58^\circ) = \frac{\text{ED}}{\text{EF}} = \frac{14}{\text{EF}}\]We can multiply both sides by EF, and we get
\[EF*\tan(58^\circ) = 14\]Divide both sides by \(\tan(58^\circ)\)
\[EF = \frac{14}{\tan(58^\circ)}\approx\frac{14}{1.6} =8.75 \]

Answer 16

@primadonnagirl123 Does that make sense?