Geometry Question Part A?

Question

10 points will go to correct and most informative answer with thumbs up as well. There are 2 questions from me this week to get the maximum amount of possible points for you guys. Here is the 1st question

Two surveyors were trying to find the difference in height between Pilgreen Place and Patterson Place. They were able to get a few measurements, the angle of depression from the top of Pilgreen Place to the base of Patterson Palace is 37 degrees, also they found that Pilgreen Place is exactly 100m tall. Finally a key piece of information...the ANGLE OF DEPRESSION from the top of Patterson Place to the top of Pilgreen Place is 55 degrees. What is the difference in height between the two buildings?

Here is a link to reference too. http://i58.photobucket.com/albums/g254/poker5495/POWVII.jpg

Answer 1

The angle from the top of the shorter building to the base of the other building forms a right triangle, where one leg is the height of the shorter building and the other is the distance between the two buildings.

tan(37) = 100/x, where x is the distance between the two buildings.

Solving for x, we get x = 132.7 feet.

The angle from the roof of the taller building to the roof of the shorter one forms another right triangle, where one leg is the distance between the two buildings, and the other is the difference in height between the two buildings.

tan(55) = y/x, where x is the distance between the two buildings, and y is the difference in building heights

tan(55) = y/132.7

Solving for y, we get the difference in height between the two buildings is about 189.5 feet.

Answer 2

The answer is 18 degrees.