Question

the length of a shadow of a building is 30 m. the distance from the top of the building to the tip of the shadow is 36 m. find the height of the building. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Identify the triangle type

The building, its shadow, and the line from the top of the building to the tip of the shadow form a right - triangle. Let the height of the building be \(h\), the length of the shadow \(b = 30\) m, and the hypotenuse \(c=36\) m. We can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a\) is the height of the building (the unknown side we want to find). Rearranging the formula to solve for \(a\), we get \(a=\sqrt{c^{2}-b^{2}}\).

Step2: Substitute the values

Substitute \(c = 36\) and \(b = 30\) into the formula: \(a=\sqrt{36^{2}-30^{2}}\). First, calculate \(36^{2}=36\times36 = 1296\) and \(30^{2}=30\times30=900\). Then, \(36^{2}-30^{2}=1296 - 900=396\).

Step3: Calculate the square root

Now, find the square root of 396: \(\sqrt{396}\approx19.9\) (rounded to the nearest tenth).

Answer:

\(19.9\)