High School

Sue measures a 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.

Calculate the height from her eye level to the top of the tree.

Answer :

Final answer:

To find the height from Sue's eye to the top of the tree, calculate the height from her eye to the base of the tree and use trigonometry to find the vertical height to the top of the tree.

Explanation:

To calculate the height from Sue's eye to the top of the tree:

  1. First, determine the height from Sue's eye to the base of the tree: 20m + 1.64m = 21.64m.
  2. Next, set up a right triangle with the distance from Sue's eye to the base as the base of the triangle (21.64m) and the vertical height from the base to the top of the tree as the height of the triangle.
  3. Use trigonometry (tan function) to find the height from Sue's eye to the top of the tree: tan(39°) = height / 20m.

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