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Nina is admiring a statue in Vindale Park. The statue is \(16\) feet taller than she is, and Nina is standing \(12\) feet away. How far is it from the top of the statue to Nina's head? $\newline$ ____feet

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Pythagorean theorem: word problems

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Q. Nina is admiring a statue in Vindale Park. The statue is \(16\) feet taller than she is, and Nina is standing \(12\) feet away. How far is it from the top of the statue to Nina's head?

\newline

____feet

Identify Problem: Identify the problem as a right triangle problem where Nina's height plus $16$ feet is one leg, and $12$ feet is the other leg. The distance from the top of the statue to Nina's head is the hypotenuse.
Define Variables: Let Nina's height be $h$ feet. Then, the statue's height is $h + 16$ feet. The distance from Nina to the base of the statue is $12$ feet. We need to find the hypotenuse $d$ of the triangle formed.
Apply Pythagorean Theorem: Using the Pythagorean Theorem: h + 16)^2 + 12^2 = d^2\. Simplify the squares: \$12^2 = 144.
Simplify Equation: Substitute the values and simplify: h + 16)^2 + 144 = d^2\. However, we don't know \$h, so we can't solve for $d$ directly. This is a mistake in our approach; we need to know Nina's height or another method to solve this.

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