Final answer:
The remaining sides of a 30°-60°-90° triangle with a hypotenuse of 7 are approximately 3.5 and 6.055, corresponding to the short side and the longer leg respectively.
Step-by-step explanation:
To find the remaining sides of a 30°-60°-90° triangle with the longest side (hypotenuse) being 7, we use the ratio that the sides of such a triangle are in: 1 : √3 : 2. The side across from the 30° angle is half the hypotenuse, and the side across from the 60° angle is √3 times the side across from the 30° angle.
The side across from the 30° angle (the shortest side) is 7/2, which equals 3.5. The side across from the 60° angle (the longer leg) is 3.5√3. To find an approximate decimal value for 3.5√3, multiply 3.5 by approximately 1.73 (which is the decimal approximation of √3), giving you 6.055. Therefore, the lengths of the remaining sides are approximately 3.5 and 6.055.