Problema Solution
The angle of depression from a point at the top of a tree to a point on the ground is 57 degrees and 45 minutes. Find the height of the tree if the line-of-sight distance from the top of the tree to the point on the ground is 34.23 feet.
Answer provided by our tutors
From the given information, we know that we are dealing with a right triangle, one of whose angles is 57 degrees and 45 minutes and a hypotenuse of 34.23. We want to find the height of the tree. We also know, by definition that the sin x=(opposite)/(hypotenuse). We know the angle, x=57.75, the hypotenuse, 34.23, and we want to find the height of the tree, the opposite side. Therefore, we can plug in what we know to find the height of the tree:
sin(57.75)=opposite/34.24
x=29.96 feet
Therefore, the height of the tree is 29.96 feet