Question

1. a 25 - foot ladder is placed 7 feet from the base of a building. the ladder reaches the roof of the building. what is the height of the building h in feet?

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle (formed by the building, the ground, and the ladder), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the ladder, \(c = 25\) ft) and \(a\) is one leg (distance from the base of the building, \(a=7\) ft), and \(b\) is the other leg (height of the building \(h\)). So, \(h^{2}+7^{2}=25^{2}\).

Step2: Simplify the equation

$$
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$$

Step3: Solve for \(h\)

Take the square root of both sides. Since \(h>0\) (height), \(h=\sqrt{576}\)

Answer:

\(24\) feet