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We are given the following information:

- Semi-vertical angle of the cone, \( \theta = 38^\circ \)
- Diameter of the base of the cone, \( d = 4 \, \text{cm} \)
  
To find the height of the cone, let's denote the following:

- Radius of the base: \( r = \frac{d}{2} = \frac{4}{2} = 2 \, \text{cm} \)
- Height of the cone: \( h \)

Using the semi-vertical angle, we know that:

\[
\tan(\theta) = \frac{r}{h}
\]

From this, we can solve for \( h \):

\[
h = \frac{r}{\tan(\theta)}
\]

Substituting the known values:

\[
h = \frac{2}{\tan(38^\circ)}
\]

Let me calculate that.The height of the cone is approximately \( h \approx 2.56 \, \text{cm} \).

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How would the height change if the semi-vertical angle increased?
2. What is the slant height of the cone given this information?
3. How can the volume of the cone be calculated from the given data?
4. What role does the semi-vertical angle play in determining the cone's dimensions?
5. How would you find the lateral surface area of the cone?

**Tip**: The semi-vertical angle helps define the proportions of the cone, linking the height to the base radius geometrically.

The semi-vertical angle of a cone is 38° and the diameter of its base is 4 cm. Find its height.

Learn how to find the height of a cone given its semi-vertical angle of 38° and a base diameter of 4 cm. This step-by-step solution involves applying trigonometric ratios and geometry concepts. Suitable for students in Grades 9-11.

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