Question

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

Explanation:

Step1: Identify the triangle type

This is a right - triangle problem, where the building height (\(h\)), shadow length (\(29\) m) and the distance from the top of the building to the tip of the shadow (\(35\) m) form a right - triangle. The distance from the top of the building to the tip of the shadow is the hypotenuse (\(c = 35\)), the shadow length is one leg (\(a=29\)), and the building height is the other leg (\(b = h\)). We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), and we need to solve for \(b\). Rearranging the formula for \(b\), we get \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

Substitute \(a = 29\) and \(c=35\) into the formula:
\(b=\sqrt{35^{2}-29^{2}}\)
First, calculate \(35^{2}=35\times35 = 1225\) and \(29^{2}=29\times29=841\). Then, \(35^{2}-29^{2}=1225 - 841=384\). So, \(b=\sqrt{384}\).

Step3: Calculate the square root

\(\sqrt{384}=\sqrt{64\times6}=8\sqrt{6}\approx8\times2.449 = 19.592\approx19.6\)

Answer:

\(19.6\)