Thank you for visiting Suppose that you are headed toward a plateau 35 9 meters high If the angle of elevation to the top of the plateau is 25. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To find out how far you are from the base of a plateau that is 35.9 meters high, given that the angle of elevation to the top is 25.5°, we can use some basic trigonometry.
### Step-by-step Solution
1. Understand the Situation: You're looking up at the top of a plateau. This creates a right triangle where:
- The height of the plateau is the opposite side (35.9 meters).
- The distance from you to the base of the plateau is the adjacent side, which we need to find.
- The angle of elevation is the angle between the ground and your line of sight to the top, which is 25.5°.
2. Trigonometric Function: We will use the tangent function because it relates the opposite side and the adjacent side in a right triangle.
[tex]\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
3. Set Up the Equation:
[tex]\[
\tan(25.5°) = \frac{35.9}{\text{distance from base}}
\][/tex]
4. Solve for the Distance from Base:
Rearrange the equation to solve for the distance:
[tex]\[
\text{distance from base} = \frac{35.9}{\tan(25.5°)}
\][/tex]
5. Calculate: Using the tangent of 25.5°, you find:
- The distance from the base is approximately 75.3 meters (rounded to one decimal place).
So, you are approximately 75.3 meters away from the base of the plateau.
### Step-by-step Solution
1. Understand the Situation: You're looking up at the top of a plateau. This creates a right triangle where:
- The height of the plateau is the opposite side (35.9 meters).
- The distance from you to the base of the plateau is the adjacent side, which we need to find.
- The angle of elevation is the angle between the ground and your line of sight to the top, which is 25.5°.
2. Trigonometric Function: We will use the tangent function because it relates the opposite side and the adjacent side in a right triangle.
[tex]\[
\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}
\][/tex]
3. Set Up the Equation:
[tex]\[
\tan(25.5°) = \frac{35.9}{\text{distance from base}}
\][/tex]
4. Solve for the Distance from Base:
Rearrange the equation to solve for the distance:
[tex]\[
\text{distance from base} = \frac{35.9}{\tan(25.5°)}
\][/tex]
5. Calculate: Using the tangent of 25.5°, you find:
- The distance from the base is approximately 75.3 meters (rounded to one decimal place).
So, you are approximately 75.3 meters away from the base of the plateau.
Thank you for reading the article Suppose that you are headed toward a plateau 35 9 meters high If the angle of elevation to the top of the plateau is 25. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
