Question

find k.
4 ft
45°
45°
k
write your answer in simplest radical form.
feet
submit

Explanation:

Step1: Identify triangle type

The triangle is a right - isosceles triangle (two angles are \(45^{\circ}\), so the two legs are equal, and hypotenuse is given as \(4\) ft). For a right - isosceles triangle with hypotenuse \(c\) and leg \(a\) (or \(k\) in this case), the relationship is \(c = a\sqrt{2}\), so \(a=\frac{c}{\sqrt{2}}\).

Step2: Solve for \(k\)

Given \(c = 4\) ft, then \(k=\frac{4}{\sqrt{2}}\). Rationalize the denominator: \(k=\frac{4\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{4\sqrt{2}}{2} = 2\sqrt{2}\).

Answer:

\(2\sqrt{2}\)