Final answer:
Using the Pythagorean theorem, the height of the display case housing the Kronosaurus skeleton is calculated to be approximately 41.3 feet to the nearest tenth, given the length of the case is 12 feet and the diagonal is 43 feet.
Step-by-step explanation:
The question relates to using the Pythagorean theorem to find the height of a rectangular display case when the length and the diagonal are known. Given that the museum features the skeleton of a foot long Kronosaurus and that the display case is designed just long enough to house the skeleton, we know that the length of the display case is approximately 12 feet. With the diagonal length being 43 feet, we use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).
In this scenario, we are solving for the height (b) with the known values: length (a) is 12 feet and the diagonal (c) is 43 feet. The calculation would look like this:
- c² = a² + b²
- 43² = 12² + b²
- 1849 = 144 + b²
- b² = 1849 - 144
- b² = 1705
- b = √1705
- b ≈ 41.3 feet (to the nearest tenth)
Therefore, the height of the display case is approximately 41.3 feet to the nearest tenth of a foot.