Question

Enter the range of values for x using the picture shown

Answer 1

We are asked to find a range for x. Let's start by finding the maximum value. We know, by definition, that a side opposite a larger angle has a longer length. For example, if you think about a right triangle, the hypotenuse (the longest side) is always opposite of the right angle (the largest angle). We are given two side lengths: 23 is opposite of 42 degrees, and 21 is opposite of 3x + 15. Because 42 is opposite the longer side, 42 degrees is a larger angle than 3x + 15. We can set up the inequality and solve for x:

$\begin{gathered} 3x+15$

Now, let's look at the minimum value. We know that the angle definitely has to be larger than 0. So, we can set up that inequality and solve for x:

$\begin{gathered} 3x+15>0 \\ 3x>-15 \\ x>-5 \end{gathered}$

Now, we have our final range: -5 < x < 9