If a \( 45^{\circ}-45^{\circ}-90^{\circ} \) triangle has a hypotenuse of 7.07 , find the length of each leg. (Round your answer to the nearest whole number.) Answer:

In a \( 45^{\circ}-45^{\circ}-90^{\circ} \) triangle, the lengths of the legs are equal, and they relate to the hypotenuse by the formula \( \text{leg} = \frac{\text{hypotenuse}}{\sqrt{2}} \). So, if the hypotenuse is 7.07, the length of each leg is \( \frac{7.07}{\sqrt{2}} \approx 5 \) (when rounded to the nearest whole number). This special triangle is a favorite in geometry because it simplifies calculations and is often used in various fields, including architecture and engineering, where right angles are crucial. Understanding its properties can make problem-solving a breeze, especially with the 45-45-90 triangle’s unique ratios!