Question

Geometry problem help please.

Answer 1

Hi @hardlyhuman are you familiar with law of cosines?

Answer 2

Hi again and a little

Answer 3

Would you mind posting it here so I know that you know it? Thanks.

Answer 4

In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

Answer 5

Yeah, but what is the law of cosines formula?

Answer 6

\(c^2 = a^2 + b^2 - 2ab\cos(C)\)

Answer 7

That's the correct form it should be remembered.

Answer 8

okay

Answer 9

Because the first part is the Pythagorean Theorem
`c^2 = a^2 + b^2` - `2ab\cos(C)`

Then you're subtracting twice the legs (a and b) and the product of the cosine of the angle.

Answer 10

ok

Answer 11

So anyway, what you can do first is draw a model triangle with the given side lengths. Click the draw feature below this chat do to so.

Answer 12

I think it's 41

Answer 13

Looks great. So now, the next step would be to smartly select your a, b, and c, values.

Answer 14

Would you mind showing the work you did to get 41?

Answer 15

No work, just making a guess

Answer 16

Explain how to "guess" 41 from the given information.

Answer 17

half of a 90 degree angle would be 45 and it looks to be a little less than that so, I thought 41

Answer 18

wait hold on, did the wrong side

Answer 19

nope, same guess

Answer 20

Nope, that is not close to logical reasoning for this one.

Answer 21

Right now, we need to assign variables for each given side a, b, and c. What variables have you assigned for each given side?

Answer 22

a=5 b=9 c=13

Answer 23

I really don't know what I'm doing here

Answer 24

I know. That was intentional. I wanted you to do it wrong so that I could explain to you how to do it right. Since we need to find the angle opposite the side that is 9 ft long we need to make that our side c. So set c = 9. Then it won't matter which a or b you assign to the other sides.

Answer 25

Let's try this again now, knowing that c = 9.

Answer 26

okay

Answer 27

A=5 B=13 C=9

Answer 28

Okay, next plug those values in to the formula. But remember, since those are side values, we use smaller case a, b, and c and know that \(C \ne c\) The big \(C\) is what we are trying to find. The big \(C\) represents the angle opposite side \(c\).

Answer 29

Is this right?

Answer 30

No, that does not reflect the formula I gave you.

Answer 31

okay, let me try this again

Answer 32

How about start with the formula I gave you and use \(\LaTeX\) to input the values.

Answer 33

is this it? c2=a2+b2−2abcos(C)

Answer 34

and I don't know what that other stuff is supposed to be

Answer 35

Typing this `\(c^2 = a^2 + b^2 - 2ab\cos(C)\)` makes this: \(c^2 = a^2 + b^2 - 2ab\cos(C)\)

Answer 36

so is that it or no?

Answer 37

I can't interpret what you wrote because you are not using the right symbols. You have to at least use the caret symbol for exponents.

Answer 38

ok

Answer 39

how would i use the caret symbol for exponents?

Answer 40

I just showed you look above

Answer 41

k

Answer 42

Alternatively you can use the equation button just below the chat.

Answer 43

That's better, but you forgot to enter the a and b values for the `2ab` portion of the formula.