Question

a 33 - m tall building casts a shadow. the distance from the top of the building to the tip of the shadow is 37 m. find the length of the shadow. if necessary, round your answer to the nearest tenth.

Explanation:

Step1: Identify the right - triangle

The building, its shadow, and the line from the top of the building to the tip of the shadow form a right - triangle. The height of the building is one leg ($a = 33$ m), the length of the shadow is the other leg (let's call it $b$), and the distance from the top of the building to the tip of the shadow is the hypotenuse ($c = 37$ m).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. We want to find $b$, so we can rewrite the formula as $b=\sqrt{c^{2}-a^{2}}$.
Substitute $a = 33$ and $c = 37$ into the formula:
\[

$$\begin{align*} b&=\sqrt{37^{2}-33^{2}}\\ &=\sqrt{(37 + 33)(37 - 33)}\\ &=\sqrt{70\times4}\\ &=\sqrt{280} \end{align*}$$

\]

Step3: Calculate the value of $b$

$\sqrt{280}\approx16.7$ m.

Answer:

$16.7$