Question

the length of a shadow of a building is 31 m. the distance from the top of the building to the tip of the shadow is 37 m. find the height of the building. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the building be \(h\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 37\) (hypotenuse), \(a=31\) (base), and \(b = h\) (height). So \(h^{2}+31^{2}=37^{2}\).

Step2: Solve for \(h^{2}\)

\(h^{2}=37^{2}-31^{2}\). Using the formula \(x^{2}-y^{2}=(x + y)(x - y)\), we have \(h^{2}=(37+31)(37 - 31)=(68)\times(6)=408\).

Step3: Find \(h\)

\(h=\sqrt{408}\approx20.2\) (rounded to the nearest tenth).

Answer:

\(20.2\)