Question

question 9
for the right triangle shown below, which of the following is an expression for y in terms of x?
\\(\sqrt{x^{2}-16}\\)
\\(\sqrt{x^{2}+8}\\)
\\(\sqrt{x^{2}+16}\\)
\\(\sqrt{16 - x^{2}}\\)
\\(\sqrt{x^{2}-8}\\)
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Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, $x$ is the hypotenuse, and the two legs are 4 and $y$. So, $4^{2}+y^{2}=x^{2}$.

Step2: Solve for $y$

$y^{2}=x^{2}-16$, then $y = \sqrt{x^{2}-16}$ (we take the positive square root since $y$ represents the length of a side of a triangle).

Answer:

$\sqrt{x^{2}-16}$