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- anonymous

Solve for the missing length and the other two angles in the triangle below.
I will add an attachment! Thank you!

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- anonymous

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- anonymous

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- anonymous

@mathmate could you help please?

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- mathmate

Typically, when two sides of a triangle and the included angle is known, you can use the cosine rule to find the third side, and then sine rule to find the remaining angles.

- anonymous

Okay the cosine rule is a^2=b^2+c^2-2bc cosA
So if I plug that in i get a^2=4^2+3^2-2(4)(3) cos(15 degrees)
a^2 is approximately 1.8
sqrt 1.8 = aproximately 1.35
Is that right??

- mathmate

Yes, 1.348251 to be closer, but yes, 1.35 is correct!

- anonymous

Thank you! I have another question that is similar to this but the cosine rule does not work. I am supposed to find length a.

- mathmate

However, you need more figures to do the sine rule calculations, or else you angles will be off!

- anonymous

For my first question. To find the angles would I set up ratios?
If so, i got 1.8/ sin(15)= 4/ sin b
Then i would cross multiply??

- mathmate

Exactly, but 1.348/sin(15)...

- anonymous

oh yeah. how about my second problem?

- mathmate

The same strategy for the second problem, since two sides and included angle are known.
The fact that 108 > 90 degrees does not matter, because cos108 will then be negative, and everything will work out.

- anonymous

So use the cosine rule?

- mathmate

Yep, cosine rule, followed by sine rule (whenever 2 sides and included angle are known).

- anonymous

I get:
a^2=13^2+11^2-2(13)(11) cos(106)
but when i plug this in i get- 368.32 and the square root it and get: 19.205 is that right?

- mathmate

I get 19.4520 , you can double check my number.
Sorry, gtg.

- anonymous

I still get 19.205 but thank you!

- mathmate

I think the angle is 108, unless I made a mistake. @haileycaroen

- mathmate

I think the angle is 108, unless I made a mistake. @HaileyJCaroen

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