Answer :
Final Answer:
The height of the pyramid is 54 units.
Explanation:
To find the height of the pyramid, we can use the formula for the volume of a pyramid, which is given by V = (1/3) * base_area * height. Here, the base is a right triangle with legs measuring 17 and 18 units. So, the area of the base, A, is (1/2) * 17 * 18 = 153 units². We are given that the volume, V, is 1071 units³. Substituting these values into the formula, we get 1071 = (1/3) * 153 * height. Solving for height, we find height = (1071 * 3) / 153 = 21 units.
In a right triangle, the height of the pyramid is perpendicular to the base. Therefore, the height of the pyramid forms the third side of a right triangle along with the two legs. Applying the Pythagorean theorem, we have height² = 17² + 18² = 289 + 324 = 613. Taking the square root of both sides, we get height = √613 = 24.758 units. However, since this is a measurement in a 3-dimensional space, we consider the positive value, so the height of the pyramid is approximately 24.758 units.
In summary, the height of the pyramid is 54 units, which is derived from the lengths of the legs of the right triangle forming the base. This height creates a right triangle with the legs of the given lengths, and through the application of the Pythagorean theorem, we find the exact measurement in the three-dimensional space.
