Question

26
45°
×2
x
45

Explanation:

Step1: Use the property of 45 - 45 - 90 triangle

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 length of one leg is 26. Let the hypotenuse be \(x\).

Step2: Apply the formula

Using the formula \(x=\frac{26}{\sin45^{\circ}}\) (since \(\sin45^{\circ}=\frac{\text{opposite}}{\text{hypotenuse}}\), and for a 45 - 45 - 90 triangle \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\)). Also, from the ratio of 45 - 45 - 90 triangle \(x = 26\sqrt{2}\)

Answer:

\(x = 26\sqrt{2}\)