A 37-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.

Answer 1

Let the length of the shadow be $x$ meters. Since the height of the building is 37 m and the distance from the top of the building to the tip of the shadow is also 37 m, triangle $ABC$ is a right triangle. [asy] fill((0,0)--(6,0)--(6,2)--(0,0)--cycle,mediumgray); draw((0,0)--(6,0)--(6,2)--(0,0)); dot((0,0)^^(6,0)^^(6,2)); label("$A$",(0,0),W); label("$B$",(6,0),E); label("$C$",(6,2),N); label("$37$",((0,0)+(6,0))/2,S); label("$37$",(6,2)+(-0.25,-0.35),S); [/asy] Using the Pythagorean Theorem, we can set up the equation \begin{align*}
BC^2+AC^2&=AB^2\quad\Rightarrow\quad 37^2+x^2=37^2\\
&\Rightarrow\quad x^2=0\\
&\Rightarrow\quad x=\boxed{0\text{ m}}.
\end{align*} Therefore, the length of the shadow is 0 m.