# Thread: I'm stuck with some easy trigonometry

1. ## I'm stuck with some easy trigonometry

I cant figure out the answers to these questions:

If this triangle has an area of 24cm^2, what is the value of angle D? http://i431.photobucket.com/albums/q...signmentq8.jpg

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Find the largest angle of this triangle:
http://i431.photobucket.com/albums/q...ignmentq10.jpg

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Please show working in a simple way, I'm not too good at this and I really want to understand trigonometry.

2. Originally Posted by ibenot1337
I cant figure out the answers to these questions:

If this triangle has an area of 24cm^2, what is the value of angle D? http://i431.photobucket.com/albums/q...signmentq8.jpg

---

Find the largest angle of this triangle:
http://i431.photobucket.com/albums/q...ignmentq10.jpg

---

Please show working in a simple way, I'm not too good at this and I really want to understand trigonometry.
$\displaystyle A = \frac{1}{2}acsin(B)$

3. Let's change this up... A is B, B is C and C is A
Get the formula:
$\displaystyle a^2=b^2+c^2-2bc cosA$

transpose it since we want to find angles:

$\displaystyle a^2 + 2bcCosA=b^2+c^2$

$\displaystyle =2bcCosA=b^2+C^2-a^2$

$\displaystyle =CosA = \frac {b^2+c^2-a^2}{2bc}$

you with me?

alright time to substitute. You should know that the side opposite the angle will be the "corresponding" letter.

$\displaystyle CosA = \frac {9^2 + 15^2 - 10^2}{2*9*15}$

$\displaystyle CosA= \frac {206}{270}$

$\displaystyle CosA = 0.7629$

$\displaystyle A= Cos^-1 (0.7629)$

$\displaystyle A= 40'16'$

Now just do that for B one. Add A and B then subtract from 180. You have all your angles.
If anything is wrong here please correct me as I am in the stages of learning this too...

4. Originally Posted by ibenot1337
I cant figure out the answers to these questions:

If this triangle has an area of 24cm^2, what is the value of angle D? http://i431.photobucket.com/albums/q...signmentq8.jpg
You have already got a hint for this first problem from $\displaystyle \mathrm{e}^{\mathrm{i}\pi}$, so I won't elaborate on this one any further.

Find the largest angle of this triangle:
http://i431.photobucket.com/albums/q...ignmentq10.jpg

Please show working in a simple way, I'm not too good at this and I really want to understand trigonometry.
Because the largest angle of a triangle is always opposite to the longest side, you are, in effect, asked to determine the angle at vertex A. Let me call this angle $\displaystyle \alpha$.
Now the law of cosine says that
$\displaystyle a^2=b^2+c^2-2\cdot b\cdot c\cdot\cos(\alpha)$
where a, b, and c is the length of the side opposite to vertex A, B, and C, respectively.
Since all values in this equation, with the sole exception of $\displaystyle \alpha$, are given, you can simply solve for $\displaystyle \alpha$, like this:
$\displaystyle \alpha = \cos^{-1}\frac{b^2+c^2-a^2}{2\cdot b\cdot c}=\cos^{-1}\frac{10^2+9^2-15^2}{2\cdot 10\cdot 9}=\cos^{-1}\left(-\tfrac{11}{45}\right)\approx 104.15^\circ$
and are done!

5. For the first one use the formula above. I'll assume that B is D.

$\displaystyle A = \frac{1}{2}acsin(B)$

transpose it to make SinB by itself:

$\displaystyle 24=\frac {1}{2}acsin(B)$
$\displaystyle \frac {48}{ac} = SinB$

ok all done.

$\displaystyle \frac {48}{56} = SinB$

You can do the rest..

6. ## Thanks

Thank you for all your help.

I now understand the rules I need to solve those sorts of problems.