I sorry I am very confused about why the answer question 5 on page 28 is A would you help me please?

Sure. Here’s the question:

This question appears in the plugging in chapter, so the solution (page 301) approaches it that way. I also plug in when I solve this question in the video solutions available to Math Guide Owners. So in this post, I’ll approach the question algebraically.

If you use the Pythagorean theorem, you know that:


Since the value of \sin A will be opposite leg over hypotenuse, it will be equal to \dfrac{a}{AC}. Substituting for AC based on the Pythagorean theorem calculation above gives you choice A.

    \begin{align*}\sin A&=\dfrac{a}{AC}\\\\\sin A&=\dfrac{a}{\sqrt{9+a^2}}\end{align*}

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