Question

a 29 - m tall building casts a shadow. the distance from the top of the building to the tip of the shadow is 35 m. find the length of the shadow. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the length of the shadow be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 35\) (hypotenuse), \(a=29\) (one - leg), and \(b = x\) (the other leg). So \(x=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 35\) and \(a = 29\) into the formula: \(x=\sqrt{35^{2}-29^{2}}=\sqrt{(35 + 29)(35 - 29)}\) (using \(a^{2}-b^{2}=(a + b)(a - b)\)). Then \(x=\sqrt{64\times6}=\sqrt{384}\).

Step3: Calculate the square - root

\(\sqrt{384}\approx19.6\)

Answer:

\(19.6\)