The first side of a triangle measures 5 in. less than the second side, the third side is 3 in, more than the first side, and the
1 answer:
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Notice the picture,
recall your SOH, CAH, TOA
you have,
opposite side, 165
adjacent side, 50
and the angle
that means, we'll need Mrs. tangent
thus
![\bf tan(\theta)=\cfrac{opposite}{adjacent}\implies tan(\theta)=\cfrac{165}{50} \\ \quad \\ tan^{-1}\left[ tan(\theta) \right]=tan^{-1}\left[ \cfrac{165}{50} \right] \\ \quad \\ \theta=tan^{-1}\left[ \cfrac{165}{50}\right] \\ \uparrow \\ \textit{angle of elevation}\iff\textit{angle of depression}](https://tex.z-dn.net/?f=%5Cbf%20tan%28%5Ctheta%29%3D%5Ccfrac%7Bopposite%7D%7Badjacent%7D%5Cimplies%20tan%28%5Ctheta%29%3D%5Ccfrac%7B165%7D%7B50%7D%0A%5C%5C%20%5Cquad%20%5C%5C%0A%20tan%5E%7B-1%7D%5Cleft%5B%20tan%28%5Ctheta%29%20%5Cright%5D%3Dtan%5E%7B-1%7D%5Cleft%5B%20%5Ccfrac%7B165%7D%7B50%7D%20%5Cright%5D%0A%5C%5C%20%5Cquad%20%5C%5C%0A%5Ctheta%3Dtan%5E%7B-1%7D%5Cleft%5B%20%5Ccfrac%7B165%7D%7B50%7D%5Cright%5D%0A%5C%5C%20%5Cuparrow%20%20%5C%5C%0A%20%5Ctextit%7Bangle%20of%20elevation%7D%5Ciff%5Ctextit%7Bangle%20of%20depression%7D)
recall your SOH, CAH, TOA
you have,
opposite side, 165
adjacent side, 50
and the angle
that means, we'll need Mrs. tangent
thus
Here we have this function:
Remember that, to find a hole, we could follow the steps as follows:
Before putting the rational function into lowest terms, we should factor the numerator and denominator. If there is the same factor in the numerator and denominator, there is a hole. Set this factor equal to zero and solve. The solution is the x-value of the hole.
We could factor the denominator asking for two numbers, whose sum is 8 and its multiplication is 15. These numbers are 5 and 3. Now, put these numbers in brackets as follows:
Now, our function can be written as:
Notice that the factor "x+3" is in the numerator and the denominator, so there is a hole in:
Now, we're asked to find the point where the hole is. So, we could replace x=-3 in the re-written function. This is:
Therefore, the hole is located at the point ( -3, 1/2).
And, the correct answer is actually A.