Question

the base of a 15 - foot ladder is 5 feet from a building. if the ladder reaches the flat roof

the height of the building is \\( \square \\) ft.
(simplify your answer. type an exact answer, using radicals as needed.)

the height of the building is approximately \\( \square \\) ft.
(round to the nearest tenth as needed.)

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the building be \(h\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 15\) (length of the ladder, hypotenuse) and \(a = 5\) (distance from the base of the ladder to the building). So \(h=\sqrt{c^{2}-a^{2}}=\sqrt{15^{2}-5^{2}}\).

Step2: Simplify the radical

$$
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$$

Step3: Approximate the value

\(\sqrt{2}\approx1.414\), so \(h = 10\sqrt{2}\approx10\times1.414 = 14.14\approx14.1\)

Answer:

The height of the building is \(10\sqrt{2}\) ft.
The height of the building is approximately \(14.1\) ft.