The height of the tree to the nearest tenth of a foot is 86.5 feet.
To calculate the height of the tree, we can use the Law of Sines. The Law of Sines states that the ratio of the side lengths of a triangle to the sine of the opposite angle is the same for all three sides.
In this case, we have triangle DET, where DE = 53.0 feet, angle D = 24 degrees, and angle E = 49 degrees. We want to find the height of the tree, which is represented by the side length opposite angle D.
Using the Law of Sines, we can write the following equation:
(DE) / sin(D) = (height of tree) / sin(E)
Substituting known values, we get:
53.0 feet / sin(24 degrees) = (height of tree) / sin(49 degrees)
Solving for the height of the tree, we get:
(height of tree) = (53.0 feet * sin(49 degrees)) / sin(24 degrees)
(height of tree) = 86.5 feet
Therefore, the height of the tree to the nearest tenth of a foot is 86.5 feet.