Question

b
45°
x
45°
5 ft
y
x =
y =

Explanation:

Step1: Identify triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the two legs are of equal length.
Since one leg is 5 ft, $x = 5$ ft.

Step2: Use Pythagorean theorem for hypotenuse

For a right - triangle with legs $a$ and $b$ and hypotenuse $c$, $c=\sqrt{a^{2}+b^{2}}$. In a 45 - 45 - 90 triangle with leg length $a = b = 5$ ft, $y=\sqrt{5^{2}+5^{2}}=\sqrt{25 + 25}=\sqrt{50}=5\sqrt{2}\approx5\times1.414 = 7.07$ ft.

Answer:

$x = 5$ ft
$y\approx7.07$ ft