Finding the length and central angle of chord

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If anyone could help me solve the following problems, I will greatly appreciate it! :D

a) Find the length of the chord intercepted by a central angle of 42degrees in a circle of radius 8ft.

I used the law of cosines for this problem and used 8 as the value for both a and b and used cos 42 degrees for cos C. I got 5.73, which is the correct answer, but is this the correct way of solving it?


b) find the measure of the central angle of a circle of radius 6ft that intercepted a chord of length 3.5ft.

What formula should I use for part b? I cannot use law of cosines, since I have two unknowns. Is it possible to use law of cosines? The correct answer is 33.9degrees, but how do I solve it?

Thank you
 
The law of cosines should work well. In part b), solve for the cosine of the angle. That's the only unknown.
 
so I can do cos C= (c^2 +a^2 -b^2)/(2ac)

I can use 3.5 for a and 6 for b, but what should I use for c? I tried plugging 3.5 and 6, but they don't work.

I tried to find c using the pythagorean theorem, but I cannot find a c value that I can use to plug into the law of cosines formula to get 33.9degrees.
 
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Please do not post the same exercise on multiple boards. It is a waste of time when somebody answers a question that has already been answered for you by somebody else somewhere else.

Read the post titled, "Read Before Posting", for more information about the guidelines for using this web site. 8-)
 
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