Question

find u.
10 ft
45°
45°
u
write your answer in simplest radical form.
feet

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the legs are equal in length, and the hypotenuse \(c\) is related to the leg \(a\) by the formula \(c = a\sqrt{2}\). Here, the two legs are of length \(10\) ft (since the non - hypotenuse sides of a 45 - 45 - 90 triangle are equal when the angles are 45° and 90°).

Step2: Apply the Pythagorean theorem

Let the two legs be \(a = 10\) and \(b = 10\). By the Pythagorean theorem \(a^{2}+b^{2}=u^{2}\). Substitute \(a = 10\) and \(b = 10\) into the formula:

$$
LATEXBLOCK0
$$

Answer:

\(10\sqrt{2}\) feet