Can anyone help me with this? I dont want answers just how to figure it out. The picture shows a triangular island. Which expression shows the value of e? f sin 65°, f cos 65°, d over cos 65 degrees, and d over sin 65 degrees.

Question

Can anyone help me with this? I dont want answers just how to figure it out.     The picture shows a triangular island. Which expression shows the value of e?  f sin 65°, f cos 65°, d over cos 65 degrees, and  d over sin 65 degrees.

anonymous · Answer

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anonymous · Answer

do u wanna know what sin and cos means?

phi · Answer

If you have time, see http://www.khanacademy.org/math/trigonometry/basic-trigonometry/basic_trig_ratios/v/basic-trigonometry

phi · Answer

here is an example of using trig to answer questions on a test http://www.khanacademy.org/math/geometry/geometry-worked-examples/v/ca-geometry--more-trig

anonymous · Answer

I know what they are. but, I don't understand it with the letters in front of the equation and stuff.

anonymous · Answer

the letters are just a way of representing the angles

phi · Answer

Which expression shows the value of e? 

You are given angle 65º, and you want to find side e

that means you need to use the trig ratio that uses side "e"
e is the hypotenuse.

which ratios use the hypotenuse ?

anonymous · Answer

sin and cos. right? sin=opp/hyp and cos=adj/hyp.

phi · Answer

yes.  now for angle 65º,  hyp is e.  what side is opp ?

anonymous · Answer

angle f. so it'd be sin65=f/e?

phi · Answer

side f.   so you have
sin65 = f/e
can you solve for e ?

anonymous · Answer

Wouldn't I have to multiply f by both sides to solve for e?

phi · Answer

if you multiply both sides by f you get
$$ f \sin65 = \frac{f}{e} \cdot f $$
which is not helpful.

on the other hand if you multiply both sides by e
$$ e \sin65 = \frac{f}{e} \cdot e $$
the e's on the right side "cancel out" because  e/e= 1

phi · Answer

now divide both sides by sin65 to get e by itself.

anonymous · Answer

Oh! okay. I get it. (: Thank you.

phi · Answer

you get e = f/sin65

but that is not one of your choices.

We should look at using cos65= d/e

anonymous · Answer

Okay, so, do the same thing but with cos65=d/e?

phi · Answer

yes.  another way to solve for e is "flip" both sides to get
$$ \frac{1}{\cos65}= \frac{e}{d} $$

phi · Answer

to "cancel out" the d on the right side, multiply by d.  To keep things equal, we multiply both sides by d.

anonymous · Answer

Okay. That makes much more sense now. Thank you so much.

phi · Answer

can you answer the question ?

anonymous · Answer

Yes. it's e=d/cos65. right?

phi · Answer

yes.