Certainly! Let's solve the equation [tex]\( A = \frac{1}{2} b h \)[/tex] for [tex]\( h \)[/tex] step-by-step.
1. Start with the given formula:
[tex]\[
A = \frac{1}{2} b h
\][/tex]
2. Eliminate the fraction by multiplying both sides of the equation by 2:
[tex]\[
2A = b h
\][/tex]
3. Isolate [tex]\( h \)[/tex] by dividing both sides of the equation by [tex]\( b \)[/tex]:
[tex]\[
h = \frac{2A}{b}
\][/tex]
Now that we have the formula for [tex]\( h \)[/tex], let's assume we are given specific values for [tex]\( A \)[/tex] and [tex]\( b \)[/tex]. For instance, let [tex]\( A = 10 \)[/tex] and [tex]\( b = 5 \)[/tex].
4. Substitute the given values into the formula:
[tex]\[
h = \frac{2 \cdot 10}{5}
\][/tex]
5. Perform the multiplication in the numerator:
[tex]\[
h = \frac{20}{5}
\][/tex]
6. Divide to find the value of [tex]\( h \)[/tex]:
[tex]\[
h = 4.0
\][/tex]
Therefore, the calculated height [tex]\( h \)[/tex] is [tex]\( 4.0 \)[/tex].
