Final answer:
Since Eva's exact height is not provided, we cannot calculate a the numerical answer. However, using the Pythagorean theorem, we can find the distance from the top of the statue to Eva's head by squaring the sum of Eva's height plus 72 feet and 65 feet, then taking the square root of that sum.
Step-by-step explanation:
The problem given is a classic case of a right triangle scenario where Eva is standing 65 feet away from the base of the statue that is 72 feet taller than her. To find the distance from the top of the statue to Eva's head, we can use the Pythagorean theorem which states that in a right 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.
Let's denote the height of Eva as h feet. The statue's height would then be h + 72 feet. The distance from the base of the statue to where Eva is standing is given as 65 feet.
To find the distance from the top of the statue to Eva's head, we are looking for the length of the hypotenuse of the right triangle formed by the height of the statue, the distance from Eva to the base of the statue, and the line from Eva's head to the top of the statue. Using the Pythagorean theorem:
- Let c be the distance from the top of the statue to Eva's head.
- Then, c² = (h + 72)² + 65².
Since we are not given Eva's exact height, we cannot calculate a numerical answer. However, if Eva's height h were provided, the calculation would be straightforward:
- Calculate the height of the statue by adding 72 feet to Eva's height.
- Next, square this value and add it to the square of 65 feet.
- Finally, take the square root of the sum to find the distance c.