In ΔABC, if the lengths of sides a and c are 8 centimeters and 16 centimeters, respectively, and the measure of is

Question

In ΔABC, if the lengths of sides a and c are 8 centimeters and 16 centimeters, respectively, and the measure of  is <C35°, what is the measure of <A to two decimal places?

plasmataco · Answer

Hint, use the law of cosine

plasmataco · Answer

a^2=b^2+c^2-2bc(cos(A))

mathstudent55 · Answer

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mathstudent55 · Answer

Does the figure look like the problem?

mathstudent55 · Answer

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mathstudent55 · Answer

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anonymous · Answer

it does now have a picture

mathstudent55 · Answer

Ok.
Notice that I have side a = 8 cm opposite angle A.
Side c = 16 cm opposite angle C.
Side b opposite angle B.
That means my figure corresponds tot eh given ifo of the problem, ok?

mathstudent55 · Answer

Are you studying the laws of sines and cosines?

anonymous · Answer

yes

mathstudent55 · Answer

If you had a problem in which you could use the law of sines or the law of cosines, and it's your choice, which law would you rather use?

mathstudent55 · Answer

Do you prefer using this (law of sines)

$\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c} $

or this (law of cosines)?

$c^2 = a^2 + b^2 - 2ab \cos C$

mathstudent55 · Answer

I have to go, so I'll just explain it to you.
Read it at your pace, and ask any questions you have.
I'll try to answer next time I'm on.

mathstudent55 · Answer

In my opinion, the law of sines is easier to use than the law of cosines.
The law of sines a simple proportion.
The law of cosines is a much longer expression.
If I have a choice, I always prefer using the law of sines.

mathstudent55 · Answer

The problem is that you are not always able to use the law of sines.
In those cases, you must use the law of cosines.

How do you know if you can use the law of sines?
It's simple. Since the law of sines is three equal ratios of the sine of an angle to the length of the opposite side, all you need to do is see if you are given a side and its opposite angle. If you do have a side and its opposite angle, then you can establish the ratio of the law of sines and solve for the other parts.

mathstudent55 · Answer

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mathstudent55 · Answer

In this problem, you were given side c and angle C.
Since you know an angle and its opposite side, you can establish the ratio of the law of sines.

$\dfrac{\sin C}{c} = \dfrac{\sin A}{a}$

Now plug in all the info you have and solve for the unknown, angle A.

$\dfrac{\sin 35 ^ \circ}{16~cm} = \dfrac{\sin A}{8~cm}$

Solve the proportion:

$\sin A = \dfrac{8~cm \times \sin 35 ^\circ}{16~cm} $

$\sin A = \dfrac{\sin 35 ^\circ}{2} $

$A = \sin^{-1} \dfrac{\sin 35^\circ}{2} $

mathstudent55 · Answer

Ok, sorry, but gtg.
Look it over and see if it makes sense to you.
If you have questions, just ask.

anonymous · Answer

Bro can u just help me out and give the answer please I have 4 more questions after this one and I'm done with the class and don't have to worry about it any more