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:

    \begin{align*}3^2+a^2&=AC^2\\9+a^2&=AC^2\\\sqrt{9+a^2}&=AC\end{align*}

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*}

Leave a Reply