Answer: 3 in.
Step-by-step explanation:
Given
The base of the triangle is [tex]3\frac{2}{5}\ inches[/tex]
The area of the triangle is [tex]5\frac{1}{10}\ inches^2[/tex]
Solve mixed fraction
Base is
[tex]=3\dfrac{2}{5}\\\\=\dfrac{17}{5}\ in.[/tex]
Area is
[tex]=5\dfrac{1}{10}\\\\=\dfrac{51}{10}\ in.^2[/tex]
The area of the triangle is given by
[tex]\Rightarrow \text{Area A=}\dfrac{1}{2}\times \text{base}\times \text{height}[/tex]
Insert the values to get the height
[tex]\Rightarrow \dfrac{51}{10}=\dfrac{1}{2}\times \dfrac{17}{5}\times \text{height}\\\\\Rightarrow \text{height}=3\ in.[/tex]
