Question

Suppose a triangle has two sides of length 3 and 4 and that the angle between these two sides is pi/3. What is the length of the third side of the triangle?

Answer 1

Are we to assume this is not a right triangle?

Answer 2

yes i think so

Answer 3

Are you studying the Law of Sines, by any chance?

Answer 4

Law of Cosines, perhaps?

Answer 5

You would need to use the Law of Cosines for this to solve for the missing side.

Answer 6

If this was your triangle (NOT a right triangle):

Answer 7

You would need the Law of Cosines to find side a, your missing side. The Law of Cosines for this set up would be this:\[a ^{2}=b ^{2}+c ^{2}-2bc(cosA)\]

Answer 8

Are you even here anymore? Am I talking to no one?

Answer 9

no i'm here

Answer 10

thank you by the way :)

Answer 11

Cool. Do you know the Law of Cosines?

Answer 12

not well but if i have the equation i can plug things in

Answer 13

Notice, also, that I converted the pi/3 to a degree measure of 60. I don't know about you, but my brain does not operate in radians. Degrees we are all familiar with. So always try to convert to degrees if you can, to make things easier.

Answer 14

alrighty

Answer 15

Now that you have the equation, you can plug in your numbers. Try it. Let me see what you come up with. Show me your answer, ok?

Answer 16

alright gimme a second

Answer 17

Make sure your calculator is in degrees for this, not radians.

Answer 18

a2=3^2+4^2−2(3)(4)(cos60)

Answer 19

that would be just plugging everything in right?

Answer 20

Go on....

Answer 21

BRB...just in case you post and I do not respond immediately.

Answer 22

a^2=9+16-24(.799)

Answer 23

Ok, the cosine of 60 is actually .5 I am not sure where you got .799

Answer 24

But everything else is good.

Answer 25

How did you get .799?

Answer 26

my calculator?

Answer 27

oh shoot i typed the wrong number my bad

Answer 28

Try it again. What do you get this time?

Answer 29

.5

Answer 30

Cool! NOW do the calculations and tell me what the length of side a is, please! ; )

Answer 31

sqrt a=sqrt .5, am i doing this right?

Answer 32

Put a wrong sign in there...let me retype...

Answer 33

\[a ^{2}=16+9-24(.5)\]\[a ^{2}=25-12\]\[a ^{2}=13\]\[a=\sqrt{13}\]

Answer 34

See that?

Answer 35

ohhhh

Answer 36

yeah i did 25-24 and then multiplied by .5

Answer 37

thank you :)

Answer 38

Watch your order of operations here. When you do these, always always do the multiplication first, then subtraction.

Answer 39

could you help me with one more questiom? yeah I always forget that part and it messes me up.

Answer 40

I would be happy to help!

Answer 41

BRB once again....just give me a sec

Answer 42

I'm just drawing the triangle