Final answer:
To find the length of the long leg of a 30-60-90 triangle with a short leg of 4.4, multiply 4.4 by √3 (≈ 1.732), resulting in approximately 7.6 when rounded to the nearest tenth.
Step-by-step explanation:
To determine the length of the long leg of a 30-60-90 right triangle when the short side is 4.4, we apply the knowledge that the ratio of the sides in a 30-60-90 triangle is 1:√3:2. The short leg corresponds to '1' in this ratio, representing the shortest side, opposite the 30° angle. The long leg, opposite the 60° angle, corresponds to '√3' in the ratio. Since the short leg has a length of 4.4, we calculate the long leg (L) using the ratio:
L = short leg × √3
L = 4.4 × √3
L ≈ 4.4 × 1.732
L ≈ 7.6208
When rounded to the nearest tenth, the length of the long leg is approximately 7.6.