Question

what is the value of x? triangle with 45°, 14, right angle, and x as hypotenuse

Explanation:

Step1: Identify Triangle Type

The triangle is a right - isosceles triangle (one angle \(90^{\circ}\), one angle \(45^{\circ}\), so the third angle is also \(45^{\circ}\)). In a \(45 - 45 - 90\) triangle, the hypotenuse \(x\) is related to the leg \(l\) by the formula \(x = l\sqrt{2}\).
Here, the leg \(l = 14\).

Step2: Calculate Hypotenuse

Substitute \(l = 14\) into the formula \(x=l\sqrt{2}\). So \(x = 14\sqrt{2}\).

Answer:

\(14\sqrt{2}\)