Question

a 35 - m tall building casts a shadow. the distance from the top of the building to the tip of the shadow is 36 m. find the length of the shadow. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the building be $a = 35$ m, the distance from the top of the building to the tip of the shadow be $c=36$ m, and the length of the shadow be $b$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, so $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

Substitute $a = 35$ and $c = 36$ into the formula: $b=\sqrt{36^{2}-35^{2}}=\sqrt{(36 + 35)(36 - 35)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $b=\sqrt{(71)\times(1)}=\sqrt{71}\approx 8.4$ m.

Answer:

$8.4$ m