A stick 1 meter long casts a shadow 1.3 meters long. A building casts a shadow 25 meters long. How tall is the building (to 2 decimal places) Question Help: Video. Submit Question

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UpStudy AI · Accepted Answer

To find the height of the building based on the lengths of the shadows, we can use the concept of similar triangles. The ratio of the height of the stick to the length of its shadow will be the same as the ratio of the height of the building to the length of its shadow.

Let $$ h $$ be the height of the building. We can set up the following proportion:

$$
\frac{\text{Height of stick}}{\text{Shadow of stick}} = \frac{\text{Height of building}}{\text{Shadow of building}}
$$

Substituting the known values:

$$
\frac{1 \text{ m}}{1.3 \text{ m}} = \frac{h}{25 \text{ m}}
$$

Now, we can cross-multiply to solve for $$ h $$:

$$
1 \cdot 25 = 1.3 \cdot h
$$

This simplifies to:

$$
25 = 1.3h
$$

Now, divide both sides by 1.3 to isolate $$ h $$:

$$
h = \frac{25}{1.3} \approx 19.23076923
$$

Rounding to two decimal places, the height of the building is:

$$
h \approx 19.23 \text{ meters}
$$

Thus, the height of the building is approximately **19.23 meters**.
The height of the building is approximately 19.23 meters.

A stick 1 meter long casts a shadow 1.3 meters long. A building casts a shadow 25 meters long. How tall is the building (to 2 decimal places) Question Help: Video. Submit Question

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