# Math Help - cosine rule

1. ## cosine rule

could any one help please..yet to be taught the cosine rule but trying to learn it myself but un sure what buttons to press on my calculator..
i have a triangle A, B,F. <A=52 side f=3000 and b=6000..i need to find the other side and two angles..
thanks
jim

2. Originally Posted by jim49990
could any one help please..yet to be taught the cosine rule but trying to learn it myself but un sure what buttons to press on my calculator..
i have a triangle A, B,F. <A=52 side f=3000 and b=6000..i need to find the other side and two angles..
thanks
jim
The cosine rule for your triangle is:

a^2=f^2+b^2-2fc cos(A),

since everything on the right hand side is a known you can find
a fairly easily.

Now the sine rule will allow you to find the remaining angles:

a/sin(A)=b/sin(B)=f/sin(F).

RonL

so would that give me a answer of 10190.00
thanks

4. Originally Posted by jim49990
so would that give me a answer of 10190.00
thanks
a^2=3000^2+6000^2-2*3000*6000 cos(52),

a^2=(9+36-36x0.61566)*1000^2=30.2232 1000^2

so:

a=sqrt(22.836)*1000~=4778.72

RonL

5. ## still stuck

sorry to be a pain but i am still struggling on what buttons to press on my calculator
jim

6. Originally Posted by jim49990
sorry to be a pain but i am still struggling on what buttons to press on my calculator
jim
Don't try to do it in one go on your calculator, they all differ and may not
behave in the same way as someone elses calculator.

Find 3000^3, and 6000^2, 3000*6000 and cos(52), these are single stage
operations then write out what what you now have to calculate.

So cos(52)=0.615661 (clear the calculator, make sure you are in degrees
mode, then enter 52 and hit the cos button to get this, write it down).

3000^2=9e6 (which means 9 * 1000000, clear the calculator enter 3000
then hit the x^2 key, or enter x 3000 =)
6000^2=3.6e7 (which means 36 *1000000, as above)

3000*6000=1.8e7 (which means 18 * 1000000)

then calculate:

9e6+3.6e7-2*3.6e7*0.61661=22836.204

then hit the square root key to get 4778.7..

RonL

7. ## many thanks

cheers mate..i owe you a drink
jim

8. ## angles

would <f =29 degrees
thanks

9. Originally Posted by jim49990
would <f =29 degrees
thanks
I make it 29.62 degrees.

Unsing the sine rule you should have:

sin(F)/f=sin(A)/a,

so

sin(F)=f*sin(A)/a=3000*sin(52)/4778.2=0.627851*0.78801=0.494752

and asin(0.494752)~=29.62 degrees

RonL

10. Hello, Jim!

Could any one help please?
Yet to be taught the cosine rule but trying to learn it myself
but unsure what buttons to press on my calculator.

I have a triangle $ABF$ with: $A = 52^o,\;f = 3000,\;b = 6000$
I need to find the other side and two angles.

To find side $a\!:\; a^2\;=\;b^2 + f^2 - 2bf\cos A$

We have: . $a^2\;=\;6000^2 + 3000^2 - 2\!\cdot\!6000\!\cdot\!3000\cos52^o$

Be sure your calculator is in degree mode.

On your calculator, enter:

. . $6000\;\;\boxed{x^2}\;\;\boxed{+}\;\;3000\;\;\boxed {x^2}\;\;\boxed{-}\;\;2\;\;\boxed{\times}\;\;6000\;\;\boxed{\times} \;\;3000\;\;\boxed{\times}\;\;\boxed{\cos}\;\;52\; \;\boxed{=}$

It is essential that you press $\boxed{=}$ at the end of this line.

. . Then press: . $\boxed{\land}\;\;0.5\;\;\boxed{=}
$

You should get: . $a\;=\;4778.722307\quad\Rightarrow\quad\boxed{a\;\a pprox\;4778.7}$

To find angle $B:\;\frac{\sin B}{b} \,=\,\frac{\sin A}{a}\quad\Rightarrow\quad \sin B \,=\,\frac{b\sin A}{a}$

We have: . $\sin B\:=\:\frac{6000\sin52^o}{4778.7}$

Enter: . $6000\;\;\boxed{\times}\;\;\boxed{\sin}\;\;52\;\;\b oxed{)}\;\;\boxed{\div}\;\;4778.7\;\;\boxed{=}$ . . . . and get: $0.989403922$

Press $\boxed{\sin^{-1}}\;\;\boxed{\text{Ans}}\;\;\boxed{=}$ . . . . and get: $81.65176939$

Hence: . $B \:\approx\:81.65^o\quad\hdots\quad \text{or: }B \:\approx\:98.35^o$ **

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If $B = 81.65^o$, then: . $F \:=\:180^o - 52^o - 81.65^o \:=\:46.35^o$

We have: . $\boxed{\begin{array}{ccc}A\:= \\ B\:= \\ F\;=\end{array}
\begin{array}{ccc}52^o \\ 81.65^o \\ 46.35^o\end{array}
\begin{array}{ccc}a\:= \\ b\:= \\ f\:=\end{array}
\begin{array}{ccc}4778.7 \\ 6000 \\ 3000\end{array}}$

But this doesn't check out . . .

. . $\frac{a}{\sin A} \:=\:\frac{4778.7}{\sin52^o} \:\approx\:6064.257$

. . $\frac{b}{\sin B} \:=\:\frac{6000}{\sin81.35^o} \:\approx\:6064.284$

. . $\frac{f}{\sin F}$ $\:=\:\frac{3000}{\sin46.35^o}\:\approx\:4146.110$ ??

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

**

Whenever we use $\boxed{\sin^{-1}}$, there are always two possible answers.
One is the acute angle on your calculator screen,
. . the other is its supplement (subtract from 180°)

The calculator said $B = 81.65^o$, which didn't work.
. . So it must be: . $B \:=\:180^o - 81.65^o \:=\:98.35^o$

If $B = 98.35^o$, then $F\:=\:180^o - 52^o - 98.35^o \:=\:29.65^o$

The solution is: . $\boxed{\begin{array}{ccc}A\:=\\B\:=\\F\:=\end{arra y}
\begin{array}{ccc}52^o\\98.35^o\\29.65^o\end{array }
\begin{array}{ccc}a\:=\\b\:=\\f\:=\end{array}
\begin{array}{ccc}4778.7 \\ 6000 \\ 3000\end{array}}$

. . and these check out . . .