Answer:
3 units
Step-by-step explanation:
The base of the given triangular prism is an isosceles triangle.
An isosceles triangle is made up of two congruent right triangles, each with a base equal to half the base of the isosceles triangle. So, in this case, we have two right triangles, each with a base of 4 units and a hypotenuse of 5 units.
The height of the isosceles triangle is equivalent to the height of the congruent right triangles.
To find the height (h), we can use the Pythagorean Theorem.
[tex]h^2 + 4^2 = 5^2\\\\h^2+16=25\\\\h^2=25-16\\\\h^2=9\\\\h = 3[/tex]
Therefore, the height of the triangular prism is:
[tex]\LARGE\boxed{\boxed{3\; \sf units}}[/tex]
