Question

Find c in the diagram below. Round your answer to the nearest tenth.

Answer 1

Have you studied the Law of Cosines?

Answer 2

@Sarah-Vita

Answer 3

Yes, but I really struggle with it.

Answer 4

Post a copy of the Law of Cosines from your text here so that we can use it on this problem.

Answer 5

Hang on...

Answer 6

ok

Answer 7

*From my text book*
"Cosine of an Angle: In a right triangle, the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse."

Answer 8

That is not the Law of Cosines. That is the right triangle definition of the cosine of an acute angle of a right triangle.

Answer 9

The triangle you posted is not right.

Answer 10

That is all I could find on cosines and angles in my book. There isn't anymore on cosines than that.

Answer 11

What course is this that you are taking?

Answer 12

Saxon Geometry.

Answer 13

Oh, I think I found it! :D

Answer 14

Hang on while I type it out.

Answer 15

a2 = b2 + c2 – 2bc (cos A)
b2 = a2 + c2 – 2ac (cos B)
c2 = a2 + b2 – 2ab (cos C)

Answer 16

Refresh your browser and the diamond question marks will clear up.

Answer 17

Diamond question marks?

Answer 18

In words, those three formulas can be said as this:

The square of one side of a triangle is equal to the sum of the squares of the other two sides of the triangle minus twice the product of those two sides and the cosine of the angle between them.

Answer 19

>>Diamond question marks?

Answer 20

Given that,

c^2 = 21^2 + 13^2 - 2*21*13* (cos 80 deg)

Answer 21

We have to solve that for c.

Answer 22

So, c is: 21^2 + 13^2 - 2*21*13* (cos 80 deg) ?

Answer 23

Almost:

c is: c^2 = 21^2 + 13^2 - 2*21*13* (cos 80 deg)

Answer 24

Which results in: 515.188094994, yes?

Answer 25

I do not know. I have not started working the problem.

How did you get 515.188094994 ?

Answer 26

Oh.
I entered: c^2 = 21^2 + 13^2 - 2*21*13* (cos 80 deg) into my calculator.

Answer 27

And, you got this for c? 515.188094994

Answer 28

Yes.

Answer 29

That is not c; that is c^2.

Now, take the positive square root of that to get c.

Answer 30

Positive square root of 515.188094994?

Answer 31

Yes. The side of a triangle cannot be negative.

If you punch the square root button, you'll get the positive square root by default.

Answer 32

22.6977552854

Answer 33

Correct. And, what is that to the nearest tenth?

Answer 34

23?

Answer 35

No, that is to the nearest integer.

Answer 36

22.6 --> 977552854

nearest tenth

Answer 37

Oh! Nearest tenth would be to the right of the decimal, right? Which means 22.7?

Answer 38

22.7, yes.

Answer 39

So c=22.7! ^_^

Answer 40

Yes, to the nearest tenth.

Answer 41

Thanks!!! :D

Answer 42

You are welcome.

Answer 43

^_^