Question

for the blue right triangle with a 45° angle: side length is $8\sqrt{2}$ inches, find the values of m and n.
for the green right triangle with a 45° angle: one leg length is 14, find the values of x and y.

Explanation:

Step1: Solve green triangle (x)

This is a 45-45-90 triangle, so legs are equal.
$x = 14$

Step2: Solve green triangle (y)

Hypotenuse = leg $\times \sqrt{2}$
$y = 14\sqrt{2}$

Step3: Solve blue triangle (m)

Leg = $\frac{\text{hypotenuse}}{\sqrt{2}}$
$m = \frac{8\sqrt{2}}{\sqrt{2}} = 8$

Step4: Solve blue triangle (n)

Legs are equal in 45-45-90 triangle.
$n = 8$

Answer:

$x = 14$, $y = 14\sqrt{2}$
$m = 8$ inches, $n = 8$ inches