Question

find u.
triangle image with right angle, 45° angles, 13 km side
write your answer in simplest radical form.
blank kilometers
√ button

Explanation:

Step1: Identify Triangle Type

The triangle is a right - isosceles triangle (two angles are \(45^{\circ}\), one right angle). In a \(45 - 45 - 90\) triangle, the legs are equal, and the hypotenuse \(c\) is related to the leg \(a\) by \(c=a\sqrt{2}\). Here, the leg length is \(13\) km, and \(u\) is the hypotenuse.

Step2: Apply \(45 - 45 - 90\) Triangle Formula

For a \(45 - 45 - 90\) triangle, if the length of each leg is \(a\), the hypotenuse \(c=a\sqrt{2}\). Given \(a = 13\) km, then \(u=13\sqrt{2}\) km.

Answer:

\(13\sqrt{2}\)