Question

fahim is 6 feet tall. at noon, he stands with the sun behind him casting a shadow. the distance from the top of fahims head to the furthest tip of the shadow is 13 feet. what is the length of fahims shadow? round to the nearest tenth of a foot. not drawn to scale

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, \(c = 13\) (length from head to shadow tip) and \(a=6\) (Fahim's height), and \(b = s\) (length of the shadow). So, \(s^{2}+6^{2}=13^{2}\).

Step2: Simplify the equation

\(s^{2}+36 = 169\). Then, \(s^{2}=169 - 36\).

Step3: Calculate \(s^{2}\)

\(s^{2}=133\).

Step4: Find \(s\)

\(s=\sqrt{133}\approx11.5\) (rounded to the nearest tenth).

Answer:

\(11.5\) feet