A ranch in the Australian Outback is shaped like triangle ACE, with m∠A = 42, m∠E = 103, and AC = 15 miles. Find the area of the ranch, to the nearest square mile.
I know the answer is 44 but how do i get it?

- anonymous

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- austinL

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- austinL

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- austinL

How would you solve for "h"?

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## More answers

- anonymous

soh cah toa?

- austinL

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Which one would we use?

- anonymous

sin(42)= h/15 ?

- anonymous

wait no

- austinL

Yes :)

- anonymous

oh yay wait but when you solve that isnt it negative?

- austinL

Yeah, that is odd...

- austinL

@Luigi0210

- anonymous

ahh i hate this problem

- Luigi0210

You called the camel?

- anonymous

Umm i'm not sure can you help please

- Luigi0210

Sure, hold on.
What is this?

- austinL

I know how it should work, but I arrive at a negative length for one of the sides of the triangle which is physically impossible.

- Luigi0210

Did you try:
\[A= \frac{1}{2}a*b*sinC\]

- anonymous

how does that work

- austinL

We would need to solve for another side.

- austinL

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- Luigi0210

Don't all triangles make 180?

- anonymous

so its 35 but how does that help me with side lengths

- Luigi0210

Oh, we cold use the law of sines to solve for a missing side

- austinL

Yes, but for that we need two sides (Law of Sines). As well as the additional angle which is easy to solve for.
\(\dfrac{a}{\sin(a)} = \dfrac{b}{\sin(b)} = \dfrac{c}{\sin(c)}\)

- austinL

\(\dfrac{a}{\sin(42)} = \dfrac{15}{\sin(103)}\)
We would then just solve for "a"
Then we would need to calculate for the final angle.

- Luigi0210

^ That's what I was talking about doing

- austinL

=D

- Luigi0210

I got 10.30097235

- Luigi0210

I haven't had to deal with triangles for a while.. so we put the calc in degree mode when solving right?

- austinL

Yes, because the angles are measured in degrees.

- anonymous

yea

- austinL

And yet we arrive back at the negative numbers.

- Luigi0210

Really? Is yours in radians? I got a negative answer in radians

- anonymous

yea mines in radians whoops

- austinL

10.301....
Don't I feel silly now.

- anonymous

haha smallest mistake makes the biggest difference thanks

- Luigi0210

Yup, and now you guys are set :)

- austinL

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- anonymous

thank you :D

- austinL

\(A=\dfrac{1}{2}a∗b∗\sin(C)\)
a=15
b=10.301
C=?

- anonymous

um wait would you have to split it in the middle again to make the two right triangles

- Luigi0210

Nope, you don't have to do that

- Luigi0210

C is just referring to the angle measure

- anonymous

its 35

- austinL

Correct.
C=35

- austinL

Plug and chug.

- anonymous

but don't we need to know the measure of AE?

- Luigi0210

Nope :)

- Luigi0210

Watch, you'll see the magic when you plug it in ;)

- anonymous

wait i'm confused- sorry

- austinL

\(A=\dfrac{1}{2}a∗b∗\sin(C)\)
a=15
b=10.301
C=35

- austinL

There is your area formula. You know all the parts. Boom. :)

- Luigi0210

That sinC is not the general sinx=opp/hyp
It's just sin(angle)
If that's what you're confused on

- anonymous

i got like -33 or something

- Luigi0210

Did you do it all as one?

- anonymous

wait no i got it haha THANK YOU

- austinL

\(A = \dfrac{1}{2}(15)\times10.301\times\sin(35)\)
:D

- Luigi0210

Don't thank me, thank Austin, the bike riding donkey :P

- anonymous

haha thank y'all

- austinL

You are very welcome!!

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