Cud u give me the formula of Law of Cosine on how to solve a triangle w/ 3 sides

given?

Im kind of confused with this problem:

a = 5, b = 6, c = 9

find all 3 angles A,B & C

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- Jul 29th 2006, 01:31 PM^_^Engineer_Adam^_^Law of cosine Help!!
Cud u give me the formula of Law of Cosine on how to solve a triangle w/ 3 sides

given?

Im kind of confused with this problem:

a = 5, b = 6, c = 9

find all 3 angles A,B & C - Jul 29th 2006, 02:10 PMtopsquarkQuote:

Originally Posted by**^_^Engineer_Adam^_^**

Where is the angle across from side c.

Thus .

The other formulae simply permute the values of a, b, and c and need not be given.

So for example, to find the angle across from side c we have:

Thus is second quadrant and

To find the angle across from side a, use a = 6, b = 9, c = 5. etc.

-Dan - Jul 29th 2006, 06:16 PMThePerfectHacker
You can also find the angles by using the fact that.

where,

And you can calculate area by*Heron's Formula*.

- Jul 30th 2006, 05:05 AMSoroban
Hello, Adam!

Quote:

Cud u give me the formula of Law of Cosine on how to solve a triangle w/ 3 sides given?

Im kind of confused with this problem:

a = 5, b = 6, c = 9

find all 3 angles A,B & C

No,confused . . .*I'm*

You're familiar with the Law of Cosines

. . but you'vesolved for an angle . . .__never__*ever?*

Okay, just this once . . .

I assume you know that: .

Rearrange the terms: .

Divide by . . . a formula for finding

Similarly, we can derive formulas for the other two angles:

. .

You should memorize these or be able to derive them when needed.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Your problem has: .

We have: .

. . Therefore: .

We have: .

. . Therefore: .

We have: .

. . Therefore: .

Check: .*. . . Yay!*

- Jul 30th 2006, 06:20 AM^_^Engineer_Adam^_^
Yea ...

But the only confusing thing is that after solving the law of cosine to get the 1st angle A which is 32 degrees, i solve the angle using the law of sine... so sin32 / 5 = sin C / 9 and it gave the C an angle of 72.5 degrees...

How come?

Btw

Thanks topsquart, ThePerfectHacker and thanks again Soroban!! - Jul 30th 2006, 07:03 AMSoroban
Hello again, Adam!

Quote:

After solving the Law of Cosine to get

i solved the angle using the Law of Sines.

So and it gave

How come?

You fell for a very common "trap" in these problems.

Recall that an inverse sine can have__two__possible values.

. . For example: .**or**

And your calculator gives you only the smaller value.

It is up to__you__to determine which angle is appropriate.

You got: . , but is also possible.

I've explained this to my students:

"The Law of Sines is much easier to use for determining angles.

But the Law of Sines (and your calculator) canto you.*lie*

. . (It says the angle is , but it's really

Hence, I recommend that you use the*Law of Cosines*to find angles.

. . (It doesn't lie.)"

- Jul 30th 2006, 07:11 AM^_^Engineer_Adam^_^
I c so u hav ta use cosine all the time involving 3 sides

.... thanks master soroban!! i finally found the answer to my frustration... coz i got a 20 / 50 in a seatwork with that problem...

really appreciated!