High School

We appreciate your visit to Sue measures an elevation point 20 meters from the base of a tree Using a clinometer she measures the angle of elevation to the top. 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!

Sue measures an elevation point 20 meters from the base of a tree. Using a clinometer, she measures the angle of elevation to the top of the tree, from this point, to be 39 degrees. Her height, to eye level, is 1.64 meters. What is the calculated distance to the top of the tree in the diagram?

Answer :

Final answer:

Sue's measurement involves calculating the tree's height using trigonometry. By taking the angle of elevation and the distance from the tree, along with her eye level, she can use the tangent function to determine the tree height above eye level and then add her eye height for the total tree height, which is 17.836 meters.

Explanation:

Sue needs to calculate the height of a tree using trigonometric principles. She measured the angle of elevation at 39 degrees from a point 20 meters from the base of the tree, and her eye level is 1.64 meters high.

To find the height of the tree, we will use the tangent of the angle of elevation, which relates the opposite side of the triangle (the tree's height above Sue's eye level) to the adjacent side (the horizontal distance from Sue to the tree).

Steps to Calculate the Height:

  1. Use the trigonometric formula: tangent of angle = opposite/adjacent.
  2. Calculate the opposite side: tangent(39 degrees) × 20 meters.
  3. Add Sue's eye-level height to the result to get the total tree height.

Let's perform the calculation:

tangent(39 degrees) is approximately 0.8098.
0.8098 × 20 meters = 16.196 meters (height above Sue's eye level).
Total tree height is 16.196 meters + 1.64 meters = 17.836 meters.

Thanks for taking the time to read Sue measures an elevation point 20 meters from the base of a tree Using a clinometer she measures the angle of elevation to the top. 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!

Rewritten by : Barada