Answer: [tex]\sqrt{5}[/tex] feet
Step-by-step explanation: Since it's an isosceles triangle, we can split it into two right triangles. Now we have two right triangles with a hypotenuse of 4 and one side length of 3. To solve for the other side length (the height), we can use the Pythagorean theorem. [tex]4^{2} = 3^{2} + h^{2}[/tex] where h is the height of the dog house. Solving for h, we get the answer of [tex]\sqrt{5}[/tex] feet
