Final answer:
Barbara's end of the seesaw is approximately 5.2 feet off the ground when Steve's end is touching the ground, as determined using the Pythagorean theorem.
Step-by-step explanation:
When Steve's end of the seesaw is touching the ground, the seesaw can be imagined as a right-angled triangle where the fulcrum is the peak at a height of 3 feet.
Since Barbara is sitting on the opposite end of a 12-foot-long seesaw, and the seesaw is symmetrical, the distance from the center to each end is 6 feet. Considering the seesaw like a right-angled triangle, we have a right angle where Steve is sitting, the height of the fulcrum is the opposite side of the right angle, and the length from the fulcrum to Barbara's end is the hypotenuse.
Using the Pythagorean theorem (a2 + b2 = c2), with a being the height and c being the length of the seesaw-half, or 6 feet, we can solve for Barbara's height above the ground:
- (3 feet)2 + b2 = (6 feet)2
- 9 + b2 = 36
- b2 = 36 - 9
- b2 = 27
- b = √27
- b ≈ 5.2 feet (rounded to one decimal place)
Therefore, when Steve's end of the seesaw is touching the ground, Barbara's end is approximately 5.2 feet off the ground.