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.
Using similar triangles, we can set up the proportion $\frac{x}{33}=\frac{y}{37}$ where $x$ is the length of the shadow and $y$ is the distance from the top of the building to the tip of the shadow. Cross-multiplying gives $37x=33y$. Dividing both sides by $37$ gives $x=\frac{33}{37}(37)=\boxed{33}$.
To find the length of the shadow, we can use the concept of similar triangles. The height of the building and the length of its shadow depict two sides of similar triangles.
Let's represent the length of the shadow as "x". According to the information provided, the height of the building is 33 m, and the distance from the top of the building to the tip of the shadow is 37 m.
By setting up a proportion, we can solve for the length of the shadow:
[height of building] / [distance from top of building to tip of shadow] = [length of shadow] / [distance from top of building to tip of shadow]
33 m / 37 m = x / 37 m
Now, we can solve for x by cross-multiplying:
33 m * 37 m = x * 37 m
1221 m^2 = 37x
To isolate x, we divide both sides of the equation by 37 m:
1221 m^2 / 37 m = x
Now, we can simplify the fraction and round the answer to the nearest tenth:
x ≈ 33.0 m
To find the length of the shadow, we can use the concept of similar triangles. Similar triangles have proportional sides, meaning that the ratios of corresponding sides are equal.
Let's denote the length of the shadow as "x". We can set up a proportion using the given information:
Height of building / Length of shadow = Height of shadow / Length of building
33 / x = 37 / 33
To solve for "x", we can cross-multiply:
33 * 37 = 33 * x
1221 = 33x
Divide both sides by 33:
1221 / 33 = x
The length of the shadow is approximately 37 meters.