Question

In △DEF, solve for x. Round the solution to the nearest hundredth.

(image being added shortly)

Answer 1

Do you need help?

Answer 2

yes ..

Answer 3

Start with: what is the cos 49 degrees

Answer 4

Okay, can you find our what angle F is?

Answer 5

cos of 49 degrees ? would that be something like x/55 ? omg i dont know lol ...

Answer 6

Don't really need angle F. Just go with cos of an angle is adjacent side over the hypotenuse.

Answer 7

Find angle F, Angle F would be 49+90=x
180-x = Angle F

Answer 8

Yes! @LaynaMae , you are on the right track! Now, just solve for "x"!

Answer 9

Then use the laws of sine. It is a lot simpler than using cosines.

Answer 10

okay , i'm going to solve for x ... just give me a minute (: lol

Answer 11

Forget about angle F! It is a totally unnecessary step! @LaynaMae , you are almost at the solution with your last post.

Answer 12

unfortunately i don't know how to solve for 'x' .... i thought i did ... :( it's driving me crazyy ...

Answer 13

According to your second to last post, you correctly said that cos 49 degrees = x/55. If you multiply both sides by 55, you have your "x".

Answer 14

This is what I was proposing. All angles inside a triangle have to add up to 180. Therefore F has to be 41 degrees. Now take the sine of 41 over x and set that equal to sin of 90 over 55

Answer 15

That will give you your answer.

Answer 16

so multiply 49 by 55 and x by 55 .....?

Answer 17

(55)(cos 49 degrees) = x and then you are done. @zordoloom , that is correct, but not necessary as the angle for which you can take the cosine is already given, so you don't have to go through extra steps.

Answer 18

@zordoloom , that is about 3 times the work you need to do just to get "x". You have to get sines for 2 angles and then work the algebra. Way too much work. My way is much simpler and straightforward!

Answer 19

I just mention the law of sines because that is what most student learn first. Its simple.

Answer 20

wait , so im multiplying 55 by x/55 ? im so confused ...

Answer 21

It is an excellent thing to know, granted. But it doesn't apply here. You are just going to confuse her in that she will think she has to go through all of that every time when the answer is gotten in my one step.

Just:
(55) times (cos 49 degrees) = x That's it! And then you are completely done.

Answer 22

You either leave the answer as (55)(cos 49 degrees) = x or you set your calculator to "degrees", get the cos, multiply by 55 and then you have "x".

Answer 23

I'll leave this up to the person who asked the question. Which ever method you prefer, you can use. They both are good, but @tcarroll010's method is more efficient.

Answer 24

okay soooo .... im still kind of confused . im probably over thinking it but i just dont know what to do ..

Answer 25

Do you know how to get the numerical value for cos 49 degrees? Or at least, do you understand the notation of cos 49 degrees?

Answer 26

Just plug in (55)(cos 49 degrees) or (55sin41)/sin90 into any calculator.

Answer 27

isn't what i said earlier ? lol x/55 ? that's what i have written in my notes

Answer 28

cos 49 degrees = cos (49 degrees). You have to either use a calculator to get the value (or tables) or just leave cos 49 degrees as cos 49 degrees. Then just multiply it by 55 and you have "x". That's all there is to it!

Answer 29

okay but what i dont understand is you're saying to multiply cos 49 degrees by 55 ? how would i even do that if the cos of 49 degrees IS 55 ? or do i multiply 55 by 55 ?

Answer 30

If you need an approximate x value, then x would be 36.0832...

Answer 31

You still have solve for x. You can't leave 55 under x as in x/55. If you are solving for "x", you have to isolate it all by itself. x = (55) times (cos 49 degrees) . Get x by itself whatever method you use.

Answer 32

so x=55 then ? omg ..... i'm never going to get this ..

Answer 33

@LaynaMae x=36.08 I posted it above twice.

Answer 34

Your problem stated "... solve for x ..." Therefore, your answer will be of the form "x = some expression". That is, x = (55) times (cos 49 degrees) . That's your "x = something".

I can't say it any clearer:

x = (55) times (cos 49 degrees) .

Answer 35

x = (55) times (cos 49 degrees) = (55) (0.6560...) approx. = 36.083 = x

Answer 36

okay .. i'm sorry for the hassle , but im an over-thinker . if you wanna help , you have to be patient with me

Answer 37

@LaynaMae , it is possible that your difficulty lies in understanding just what sines and cosines are. I really believe that you would benefit from going over the definition of each and the realization that they are ratios of sides of a triangle. Until you are comfortable with that, I think you will be stuck here. It's a time for "back to the fundamentals".

Answer 38

i know i have to review it some more . thanks for the help thoughh

Answer 39

You're welcome. One thing, once you have an angle, you can just plug that angle into a calculator and you will get a real number. That's all there is to it, as far as the mechanics. It is vitally important to have the concepts first though.

Answer 40

thank you !