The angle of elevation from the child to the star is 68°.
What is the concept of heights and distances?
The concept of heights and distances is the application of trigonometric ratios in real-life cases, to solve for the missing heights, distances, or the angle of sight from one point to the other.
How to solve the question?
In the question, we are informed that a star sits at the top of a 27-foot-tall Christmas tree, and it is seen by a child who is standing 11 feet away from the tree.
We are asked to find the angle of elevation from the child to the star.
We assume the 27-foot-tall Christmas tree to be AB, with the star at point A, C being the boy, and BC showing the distance between the boy and the tree to be 11 feet.
We are asked to find the angle of elevation from the child to the star, that is, we are asked to find angle C.
In triangle ABC,
tan C = AB/BC {tan θ = perpendicular/base},
or, tan C = 27/11,
or, C = tan⁻¹(27/11),
or, C = 67.83365417791754271396329239993° ≈ 68°.
Thus, the angle of elevation from the child to the star is 68°.
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