Question

find c.

(image of a right triangle with two 45° angles, one leg labeled 2 ft, hypotenuse labeled c)

write your answer in simplest radical form.

feet
(with a square root button icon)

Explanation:

Step1: Identify Triangle Type

The triangle is a right - isosceles triangle (two angles are \(45^{\circ}\), one is \(90^{\circ}\)), so the legs are equal, and the hypotenuse \(c\) can be found using the Pythagorean theorem or the \(45 - 45 - 90\) triangle ratio. The ratio for a \(45 - 45 - 90\) triangle is \(leg:leg:hypotenuse = 1:1:\sqrt{2}\).

Step2: Apply the Ratio

One leg is \(2\) ft. For a \(45 - 45 - 90\) triangle, hypotenuse \(c=\text{leg}\times\sqrt{2}\). Substituting the leg length (\(2\) ft) into the formula, we get \(c = 2\times\sqrt{2}=2\sqrt{2}\).

Answer:

\(2\sqrt{2}\)