Question

find u.
triangle with angles 45°, 45°, right angle, hypotenuse 4√2 km, side u
write your answer in simplest radical form.
blank kilometers

Explanation:

Step1: Identify triangle type

The triangle has two \(45^\circ\) angles and a right angle, so it's a 45-45-90 triangle. In a 45-45-90 triangle, the legs are equal, and the hypotenuse \(h\) is related to a leg \(l\) by \(h = l\sqrt{2}\).

Step2: Relate hypotenuse and leg

Given hypotenuse \(= 4\sqrt{2}\) km, let leg \(u\) be the unknown. From the formula \(h = l\sqrt{2}\), we solve for \(l\) (which is \(u\)):
\(u\sqrt{2}=4\sqrt{2}\)

Step3: Solve for \(u\)

Divide both sides by \(\sqrt{2}\):
\(u=\frac{4\sqrt{2}}{\sqrt{2}} = 4\)

Answer:

\(4\)