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.
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.
To find the length of the shadow, we can use the concept of similar triangles. 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, we can set up a proportion.
Let's say the length of the shadow is x.
The proportion we can write is:
37 m / x = 37 m / 37 m
Simplifying the proportion, we get:
37 m / x = 1
Cross-multiplying, we have:
37 m = x
Therefore, the length of the shadow is 37 m.
Note: No rounding is necessary in this case because the length of the shadow is given as a whole number.
To find the length of the shadow, we can use similar triangles. Let's denote the length of the shadow as "x".
We have three important lengths in this problem:
1. The height of the building, which is 37 m.
2. The length from the top of the building to the tip of the shadow, which is also 37 m.
3. The length of the shadow, denoted by "x" (the value we want to find).
Since we have a right triangle formed by the building, its shadow, and the line connecting the top of the building to the tip of the shadow, we can use the properties of similar triangles.
The two triangles formed are similar, which means their corresponding side lengths are proportional. Using this, we can set up the following equation:
height of building / length of shadow = length from top to tip of shadow / length of shadow
37 / x = 37 / (37 + x)
We can cross-multiply to get:
37 * (37 + x) = 37 * x
Simplifying the equation:
37 * 37 + 37 * x = 37 * x
37 * 37 = 37 * x - 37 * x
1369 = 0
This equation is not possible, and it implies that there is an error or inconsistency in the given information. Please double-check the values provided for the height of the building and the length from the top to the tip of the shadow.