Answer :
To find the distance from the base of the plateau when you know the height of the plateau and the angle of elevation, you can use trigonometry, specifically the tangent function.
Here's how to solve it step-by-step:
1. Identify the Right Triangle:
- In this scenario, you are forming a right triangle with the plateau.
- The height of the plateau (39.1 meters) is the opposite side of the angle of elevation.
- The distance from you to the base of the plateau is the adjacent side.
2. Use the Tangent Function:
- The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
- Mathematically, this is written as:
[tex]\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
3. Rearrange to Find Distance:
- We need to find the adjacent side, which is the distance from the base of the plateau. Rearrange the formula to solve for the adjacent side:
[tex]\[
\text{adjacent} = \frac{\text{opposite}}{\tan(\text{angle})}
\][/tex]
4. Substitute Known Values:
- Plug in the known values:
- Opposite side (height of the plateau): 39.1 meters
- Angle of elevation: 28.5 degrees
5. Convert Angle to Radians:
- Trigonometric functions often require angles to be in radians for calculations. Convert 28.5 degrees to radians.
6. Calculate the Distance:
- Use the tangent function to find the distance:
[tex]\[
\text{distance} = \frac{39.1}{\tan(28.5^\circ)}
\][/tex]
7. Find the Solution:
- After performing these steps, you get approximately 72.0 meters when you round to one decimal place.
Therefore, the distance from the base of the plateau is approximately 72.0 meters.
Here's how to solve it step-by-step:
1. Identify the Right Triangle:
- In this scenario, you are forming a right triangle with the plateau.
- The height of the plateau (39.1 meters) is the opposite side of the angle of elevation.
- The distance from you to the base of the plateau is the adjacent side.
2. Use the Tangent Function:
- The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
- Mathematically, this is written as:
[tex]\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
3. Rearrange to Find Distance:
- We need to find the adjacent side, which is the distance from the base of the plateau. Rearrange the formula to solve for the adjacent side:
[tex]\[
\text{adjacent} = \frac{\text{opposite}}{\tan(\text{angle})}
\][/tex]
4. Substitute Known Values:
- Plug in the known values:
- Opposite side (height of the plateau): 39.1 meters
- Angle of elevation: 28.5 degrees
5. Convert Angle to Radians:
- Trigonometric functions often require angles to be in radians for calculations. Convert 28.5 degrees to radians.
6. Calculate the Distance:
- Use the tangent function to find the distance:
[tex]\[
\text{distance} = \frac{39.1}{\tan(28.5^\circ)}
\][/tex]
7. Find the Solution:
- After performing these steps, you get approximately 72.0 meters when you round to one decimal place.
Therefore, the distance from the base of the plateau is approximately 72.0 meters.
