To find the height of the triangle when given the base and the area, we can use the area formula for a triangle, which is:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
We are given:
- The base [tex]\( b \)[/tex] is 11 inches.
- The area [tex]\( A \)[/tex] is 49.5 square inches.
Let's plug these values into the formula and solve for the height [tex]\( h \)[/tex].
[tex]\[ 49.5 = \frac{1}{2} \times 11 \times h \][/tex]
First, isolate the height [tex]\( h \)[/tex] by multiplying both sides of the equation by 2 to remove the fraction:
[tex]\[ 2 \times 49.5 = 11 \times h \][/tex]
[tex]\[ 99 = 11 \times h \][/tex]
Next, solve for [tex]\( h \)[/tex] by dividing both sides by 11:
[tex]\[ h = \frac{99}{11} \][/tex]
[tex]\[ h = 9 \][/tex]
So, the height of the triangle is 9 inches.
Therefore, the correct answer is:
[tex]\[ \boxed{9} \][/tex]
