Sure, let's solve for the height [tex]\( h \)[/tex] step by step using the given formula for the area of a triangle.
The formula for the area ([tex]\( A \)[/tex]) of a triangle is:
[tex]\[ A = \frac{1}{2} b h \][/tex]
Here, [tex]\( A \)[/tex] represents the area of the triangle, [tex]\( b \)[/tex] represents the base of the triangle, and [tex]\( h \)[/tex] represents the height of the triangle. We need to rearrange this formula to solve for [tex]\( h \)[/tex].
1. Write down the original formula:
[tex]\[ A = \frac{1}{2} b h \][/tex]
2. Isolate the term with [tex]\( h \)[/tex] on one side of the equation.
To do this, we need to get rid of the fraction [tex]\(\frac{1}{2}\)[/tex]. We can do this by multiplying both sides of the equation by 2 to eliminate the fraction.
[tex]\[ 2A = 2 \left(\frac{1}{2} b h\right) \][/tex]
Simplifying the right-hand side, we get:
[tex]\[ 2A = b h \][/tex]
3. Solve for [tex]\( h \)[/tex].
To isolate [tex]\( h \)[/tex], divide both sides of the equation by [tex]\( b \)[/tex]:
[tex]\[ h = \frac{2A}{b} \][/tex]
So, the height [tex]\( h \)[/tex] can be found using the formula:
[tex]\[ h = \frac{2A}{b} \][/tex]
This equation shows that the height [tex]\( h \)[/tex] of a triangle is twice the area [tex]\( A \)[/tex] divided by the base [tex]\( b \)[/tex].
