Question

the length of a shadow of a building is 9 m. the distance from the top of the building to the tip of the shadow is 15 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 $c = 15$ (distance from top of building to tip of shadow), $a=9$ (length of shadow), and $b = h$ (height of building). So $h=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 9$ and $c=15$ into the formula: $h=\sqrt{15^{2}-9^{2}}=\sqrt{(15 + 9)(15 - 9)}=\sqrt{24\times6}=\sqrt{144}$.

Step3: Calculate the result

$\sqrt{144}=12$.

Answer:

$12$