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To solve for the height of the building in the triangle, we can use trigonometric ratios. Here, the problem provides:

1. The base of the triangle (adjacent side) is \(48 \, \text{m}\).
2. The angle at the base is \(60^\circ\).
3. We want to find the height of the building, which corresponds to the opposite side of the \(60^\circ\) angle.

### Solution
Using the tangent function:
\[
\tan(60^\circ) = \frac{\text{opposite}}{\text{adjacent}}
\]
Let \(h\) be the height (opposite side). Then:
\[
\tan(60^\circ) = \frac{h}{48}
\]
Since \(\tan(60^\circ) = \sqrt{3} \approx 1.732\), we get:
\[
1.732 = \frac{h}{48}
\]
Multiplying both sides by \(48\):
\[
h = 1.732 \times 48
\]
\[
h \approx 83.14 \, \text{m}
\]

### Answer
The height of the building is approximately **83.14 meters**.

Would you like further details, or do you have any questions?

---

1. What is the tangent function and how is it applied in other triangle problems?
2. How would the answer change if the angle was different?
3. Can we solve this problem using sine or cosine? If yes, how?
4. How does trigonometry apply to real-world building height calculations?
5. Why is it useful to approximate values in trigonometry?

**Tip:** In trigonometry, it's essential to remember the primary functions (sine, cosine, and tangent) and how each applies to different sides in a right triangle.

Calcule la altura del edificio en la figura dada, donde la base es de 48 metros y el ángulo entre la base y la hipotenusa es de 60 grados.

Learn how to calculate the height of a building using trigonometric functions, given a right triangle with a 48-meter base and a 60-degree angle. This example covers trigonometry concepts and is suitable for high school students.

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