To determine the height of Rainee's triangle, we can use the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
We are given the following values:
- Area = 43.75 square inches
- Base = 7 inches
We need to find the height. Let's denote the height as \( h \). Substituting the given values into the formula, we have:
\[ 43.75 = \frac{1}{2} \times 7 \times h \]
Now, multiply both sides of the equation by 2 to get rid of the fraction:
\[ 2 \times 43.75 = 7 \times h \]
This simplifies to:
\[ 87.5 = 7h \]
Next, divide both sides by 7 to solve for \( h \):
\[ h = \frac{87.5}{7} \]
Calculating this gives:
\[ h = 12.5 \]
Thus, the height of Rainee's triangle is:
\[ \boxed{12.5} \text{ inches} \]