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
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
Hello, Adam!
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, I'm confused . . .
You're familiar with the Law of Cosines
. . but you've never solved for an angle . . . 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!
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!!
Hello again, Adam!
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) can lie to you.
. . (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.)"