Question

25 triangle xyz is shown below what is the vertical distance between x and y? x z y 4

Explanation:

Step1: Identify known values

Right triangle: hypotenuse $XZ=\sqrt{21}$, leg $YZ=4$, vertical leg $XY=?$

Step2: Apply Pythagorean theorem

For right triangle $XYZ$, $XY^2 + YZ^2 = XZ^2$

Step3: Solve for $XY^2$

$XY^2 = XZ^2 - YZ^2 = (\sqrt{21})^2 - 4^2 = 21 - 16 = 5$

Step4: Calculate $XY$

$XY = \sqrt{5}$

Answer:

$\sqrt{5}$