Fundamentals of Engineering Exam Review of Law of Cosines

In this episode of Engineer In Training Exam TV, Justin walks you through a Fundamentals of Engineering Exam Review of Law of Cosines.

We will begin by defining the Law of Cosines and then run through a couple of instances in which we can use the law of cosines to solve for any unknown characteristics of a triangle.

This review of Law of Cosines is part of the global subject Mathematics.

Having served over 1.5 million lessons in 150 different countries, it’s safe to say we have been in the trenches.

In the trenches working with those who are taking the exam for the first time, either fresh out of college or having taken a few years off from the books.

In the trenches working with those who have already attempted the exam, maybe multiple times, and can’t seem to crack the code.

In the trenches working with those who have been away from the books for ages, from standardized testing for the same amount of time, and can’t fathom taking on this beast of an exam.

And every iteration in between.

Every student’s situation is unique, but the building blocks of what success looks like are always the same.

Click below to register for the FREE myFE Exam Academy Course.

Once you are registered, you’ll get instant access to a proven roadmap, strategies and tactics…

Straight to your email box.

Transcription

Hey what’s going on everyone, it’s Justin Dickmeyer from EngineerInTrainingExam.com.

In today’s video we are going to present a Fundamentals of Engineering Exam Review of Law of Cosines.

We’ll start off this tutorial discussing the theory and then get in to working a problem.

So let’s start off our Fundamentals of Engineering Exam Review of Law of Cosines by defining exactly what Law of Cosines is.

We use the law of cosines and the law of sines to

solve triangles that are not right

angled such triangles are called oblique

triangles the law of cosines is use much

more frequently than the law of sines is

and more specifically when we know two

sides of a given triangle and the angle

in between those two sides then the law

of cosines enables us to determine the

third side of that triangle so let’s

illustrate the definition of the law of

cosines let’s look at the triangle here

say we have a triangle and this is side

a we got side B and we got C and this

angle right here side c so the log

cosine states that c squared is equal to

a squared plus B squared minus to a B

cosine of C so let’s look at a quick

example of how the law of cosines can be

used let’s look at the triangle again

say that we’re given that this side is

eight we’re given that this side right

here is 10 we don’t know this side which

is d let’s say that this angle D is 60

degrees and this is angle f and this is

angle e which are both unknowns but

since we have two sides eight and 10 and

the angle between those two sides we are

able to employ the law of cosines to

determine what the third side is so

let’s go ahead and just plug all of our

numbers into the into our equation d

squared is equal to e squared plus F

squared minus 2 e F cosine of D so

that’s our that’s our standard equation

we just want to plug in all that we know

so let’s just go ahead this is angle e

so opposite is going to be side e which

is going to be this first term which is

going to be a squared plus 10 squared

minus 2 times 8 times 10 cosine of 60

and so we can just use our calculators

and calculate this out it comes down to

d squared is equal to 80 for taking the

square root we get d is equal to 9.17 so

that is the length of our third unknown

side so how do we remember the equation

of the law of cosines are there is one

thing we can do is first thing we just

got to know that is it essentially is

the Pythagorean theorem with some extra

making it work for making it work for

all triangles so the Pythagorean theorem

you know is a squared plus B squared is

equal to C squared and we know that this

only works for right triangles

now the law of cosines is a squared plus

B squared minus to a B cosine of the

angle c which is equal to C squared and

this works for all triangles if you put

if you plugged in 90 degrees right here

to make this a right triangle this whole

term would disappear making it the

Pythagorean theorem so that’s basically

just how you can a quick way you can

remember what the law of cosines is so

when do you use the law of cosines

there’s there’s a two two instances in

which you could use the law of cosines

you can use it when the third side of a

triangle

I is needed needed and you know two

sides plus the angle between it also can

be used when you have when the angles of

a triangle are are needed and you know

all three sides so to use the law of

cosines essentially you need to know

there needs to be three things that you

need to know number one you need to know

either two sides and the angle between

or if you if you know all the side

you’re able to determine all the angles

within the triangle by plugging in all

your knowns so let’s again look at an

example let’s take the triangle here

let’s say we know all three sides let’s

say this side is five this side is nine

and this side is eight let’s say we have

an angle here that’s unknown a we have

an angle here B which is unknown and we

have an angle here C which is unknown so

what we want to do is determine what

let’s say angle C is so all we need to

do is start with our standard equation C

squared is equal to a squared plus B

squared minus to a B cosine of C and we

just start plugging in all of the known

sites all the known quantities that we

know so we got eight squared because

there’s a C and C is always opposite or

in this case we’re using a B and C where

before we used EF and G or yeah and so

the sides are just opposite their angles

so if this is angle C this is going to

be side see this is angle B so this is

going to be side B this is angle a so

this is going to be side a so just plug

in all your knowns eight squared is

equal to 9 squared plus 5 squared minus

two x 9 x 5 cosine of c and then all you

need to do now is calculate it out using

a calculator and you get down to the

point where it’s where it’s a see cosine

of c is equal to 42

/ 90 and then to determine what C is

just take the inverse cosine so c is

equal to cosine and negative 1 or

inverse cosine 42 / 90 and we’re going

to find that c is equal to 60 2.2

degrees so we could do that for each and

every one of the angles within that

triangle because we do know all three

sides and all three sides are defined so

using the law of cosines we can go ahead

and uh and determine more information

than what we’re given so that’s all I

got for you today guys that’s a real

quick tutorial and real basic tutorial I

hope it cleared some things up or at

least was a decent review of the subject

if you guys need any more information

regarding the engineering training exam

just go ahead and visit my site at

engineer in training exam com shoot me

an email if you have any more questions

or if you want to see any future video

tutorials on any subject it doesn’t

matter just shoot them to me and I look

forward to talking to you guys soon

alright so take care

—

Follow Prepineer Online Here:

Instagram: https://instagram.com/prepineer
Prepineer Facebook: https://facebook.com/prepineer
EngineerInTrainingExam Facebook: https://www.facebook.com/EngineerInTrainingExam
Snapchat: https://www.snapchat.com/add/prepineer
Website: https://www.Prepineer.com
Website: https://www.EngineerInTrainingExam.com
Twitter: https://twitter.com/prepineer
Passing the FE Exam – Engineering Advice (private Facebook group): https://www.facebook.com/groups/372061059925853/

Law of Cosines – Fundamentals of Engineering Exam Review

Transcription

The 12-part Academy Course

Start Our 12-Part Academy Course (It's FREE)

When to use the Chain Rule For Derivatives

How does the scheduled break work for the FE Exam?

FE Exam Practice Problem – Electrical Circuits

Transcription

The 12-part Academy Course

Reader Interactions

Leave a Reply Cancel reply

Footer

About Us

Test