Final answer:
To find the length of the hypotenuse in a 30-60-90 triangle with a side length of 3.5 ft opposite the 60° angle, you calculate twice the length of the shortest side. The shortest side is found by dividing 3.5 ft by \( \sqrt{3} \), resulting in a hypotenuse approximately 4.04 ft when rounded to the nearest hundredth.
Step-by-step explanation:
In a 30-60-90 triangle, the length of the hypotenuse is twice that of the shortest side (which is opposite the 30° angle). The side opposite the 60° angle is equal to \( \sqrt{3} \) times the shortest side. Since the side of length 3.5 ft is opposite the 60° angle, we can find the length of the shortest side by dividing 3.5 ft by \( \sqrt{3} \). Then, the hypotenuse is twice the length of the shortest side. Therefore, the length of the hypotenuse is:
Shortest Side = \( \frac{3.5}{\sqrt{3}} \)
Hypotenuse = 2 \( \times \) Shortest Side
To calculate and round to the nearest hundredth:
Hypotenuse = 2 \( \times \) \( \frac{3.5}{\sqrt{3}} \) \approx 4.04 ft