Suppose you are headed toward a plateau 

4747 

m high. If the angle of elevation to the top of the plateau is 

6060degrees°​, 

how far are you from the base of the​ plateau?




Let's solve this problem using the tangent function, similar to the previous problem.

Given:
- Height of the plateau, \( h = 4747 \) meters
- Angle of elevation, \( \theta = 60^\circ \)

We need to find the distance \( d \) from the base of the plateau.

Using the tangent function:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{d}
\]

\[
\tan(60^\circ) = \frac{4747}{d}
\]

We know that \( \tan(60^\circ) = \sqrt{3} \approx 1.732 \):

\[
d = \frac{4747}{1.732} \approx 2741.7 \text{ meters}
\]

So, you are approximately **2741.7 meters** away from the base of the plateau.

Would you like further details or have any other questions?

Here are some related questions you might find interesting:
1. How would the distance change if the angle of elevation was 30 degrees?
2. If the plateau height was reduced to 3000 meters, what would the new distance be?
3. How can you calculate the height of the plateau if the distance and angle of elevation are known?
4. What is the relationship between the angle of elevation and the distance if the height remains constant?
5. How would the distance change if the angle of elevation increased to 75 degrees?

**Tip:** The tangent function is particularly useful in solving problems involving right triangles where you have the opposite side (height) and need to find the adjacent side (distance).

Learn how to calculate the distance from the base of a plateau using the angle of elevation and given height. This problem involves trigonometric concepts, specifically using the tangent function to find distances in geometric contexts. Suitable for high school students.

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