Asolid metal cone has radius 1.65 cm and slant height 4.70 cm Find the angle the slant height makes with the base of the cone

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To determine the angle $$\theta$$ that the slant height makes with the base of the cone, we can use the relationship between the radius ($$r$$), the slant height ($$l$$), and the angle $$\theta$$ in a right triangle formed by these dimensions.

### Given:
- Radius, $$ r = 1.65 $$ cm
- Slant height, $$ l = 4.70 $$ cm

### Step-by-Step Solution:

1. **Understand the Relationship:**
   
   In a right circular cone, the slant height ($$l$$), radius ($$r$$), and height ($$h$$) form a right triangle. The angle $$\theta$$ between the slant height and the base can be found using the cosine function:
   
   $$
   \cos(\theta) = \frac{r}{l}
   $$
   
2. **Calculate $$\cos(\theta)$$:**
   
   $$
   \cos(\theta) = \frac{1.65}{4.70} \approx 0.35106
   $$
   
3. **Determine $$\theta$$:**
   
   To find $$\theta$$, take the inverse cosine (arccos) of 0.35106:
   
   $$
   \theta = \cos^{-1}(0.35106)
   $$
   
   Using a calculator:
   
   $$
   \theta \approx 69.45^\circ
   $$
   
### Conclusion:

The angle that the slant height makes with the base of the cone is approximately **69.45 degrees**.
The angle between the slant height and the base of the cone is approximately 69.45 degrees.

Asolid metal cone has radius 1.65 cm and slant height 4.70 cm Find the angle the slant height makes with the base of the cone

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