Question

the length of a shadow of a building is 27 m. the distance from the top of the building to the tip of the shadow is 30 m. find the height of the building. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Let the height of the building be \(a = 27\), the distance from the top of the building to the tip of the shadow be \(c = 30\), and the length of the shadow be \(b\). Then \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(a = 27\) and \(c = 30\) into the formula: \(b=\sqrt{30^{2}-27^{2}}=\sqrt{(30 + 27)(30 - 27)}\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)).
\(=\sqrt{57\times3}=\sqrt{171}\)

Step3: Calculate the square root

\(\sqrt{171}\approx13.1\)

Answer:

\(13.1\)