Suppose you are headed toward a plateau

5959

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?

To find the distance from the base of the plateau, we can use trigonometry. Specifically, we'll use the tangent function, which relates the angle of elevation to the height of the plateau and the distance from the base.

Given:
- Height of the plateau, \( h = 5959 \) meters
- Angle of elevation, \( \theta = 60^\circ \)

We want to find the distance from the base of the plateau, denoted as \( d \).

The tangent of the angle of elevation is given by:

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

So,

\[
\tan(60^\circ) = \frac{5959}{d}
\]

Solving for \( d \):

\[
d = \frac{5959}{\tan(60^\circ)}
\]

Since \( \tan(60^\circ) = \sqrt{3} \approx 1.732 \):

\[
d = \frac{5959}{1.732} \approx 3441.7 \text{ meters}
\]

So, you are approximately **3441.7 meters** away from the base of the plateau.

Would you like more details on this, or have any questions?

Here are some related questions you might find interesting:
1. What if the angle of elevation was 45 degrees? How would the distance change?
2. How would the distance be affected if the plateau was 7000 meters high?
3. What trigonometric function would you use if you were given the distance and angle to find the height?
4. How can you use the cosine function in problems involving angles of elevation?
5. How would you calculate the angle of elevation if the height and distance were known?

**Tip:** Knowing the basic trigonometric functions and their relationships to angles can help solve a wide variety of problems related to angles of elevation and depression.

Learn how to calculate the distance from the base of a plateau using the angle of elevation and trigonometry. Given a plateau height of 5959 meters and an angle of elevation of 60 degrees, find the distance using the tangent function. Suitable for high school students studying trigonometry.

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