We appreciate your visit to 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 offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
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.
Thanks for taking the time to read 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 insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
