SOLUTION: If the given values in a right triangle are Cos A = 1/3 and a=2, find the hypotenuse c.

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Question 85735: If the given values in a right triangle are Cos A = 1/3 and a=2, find the
hypotenuse c.
Found 2 solutions by scianci, Edwin McCravy:
Answer by scianci(186) About Me  (Show Source):
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Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
If the given values in a right triangle are Cos A = 1/3 and a=2,
find the hypotenuse c.



We have the system of equations:

a%5E2+%2B+b%5E2+=+c%5E2
cos%28A%29+=+1%2F3

or

2%5E2+%2B+b%5E2+=+c%5E2
b%2Fc+=+1%2F3

or

4+%2B+b%5E2+=+c%5E2
c+=+3b

Now we can use substitution to solve:

4+%2B+b%5E2+=+%283b%29%5E2
4+%2B+b%5E2+=+9b%5E2
4+=+8b%5E2
1+=+2b%5E2
1%2F2+=+%282b%5E2%29%2F2
1%2F2+=+b%5E2
sqrt%281%2F2%29+=+sqrt%28b%5E2%29
sqrt%282%2F4%29+=+b
sqrt%282%29%2F2+=+b
Substitute that in c=3b
c=%283sqrt%282%29%29%2F2

Edwin