Geometry Problem?

Question

Two surveyors where trying to find the difference in height between Pilgreen Place and Patterson Palace. 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 Palace to the top of Pilgreen Place is 55 degrees. What is the difference in height between the two buildings?
http://www.e-zgeometry.com/pow/pictures/29.gif

Answer 1

There are two right triangles in this picture (that concern us):
A. The triangle formed by the lower portion of Patterson's wall, the horizontal line from the top of Pilgreen, and the hypotenuse that connects them.
B. The triangle formed by the top portion of Patterson's wall, the same horizontal line, and the hypotenuse between them.

For triangle A, the vertical side is the same length as the height of Pilgreen: 100m. Since the triangle is a right triangle, and the tangent of an angle equals the length of the opposite side divided by the length of the adjacent side,
tan 37 = 100 / h, where h is the horizontal side.

Solving this equation:
h * tan 37 = 100
h = 100 / tan 37, approx. 132.7

This gives us the distance between the two buildings, and hence the bottom side of triangle B.

The angle of elevation from Pilgreen to Patterson is the same angle as the angle of depression from Patterson to Pilgreen (if this is not immediately obvious, consider the fact that their roofs form parallel lines).

Therefore, we have a right triangle with a left side angle 55, an adjacent side 132.7, and an unknown opposite side. Again,
tan = opp/adj, so
tan 55 = x / 132.7, where x is the unknown side.

Solving,
tan 55 = x / 132.7
132.7 * tan 55 = x
x = 132.7 * tan 55, approx. 189.5

This is the difference in heights, the term you were looking for:
189.5m

Answer 2

From the question, one can conlude that Patterson is taller that Pilgreen.
First to find the distance of seperation between the two buildings,a
tan37 = 100/a
a=132.7m
Now the difference in height of the two buildings, b
tan55 = b/132.7
b=189.52m

Answer 3

I bear in mind that there is a thorem that if the two aspects of a traingle are equivalent then the attitude opposite to them additionally are comparable. Please see the thorem. So the bisectors make a isoscele traingle with the section in between the angles have been getting bisected.i visit later write you the evidence of the theorm. because of fact the each and each 0.5 of the angles are equivalent, then the completed angles are equivalent. here you got here upon the two angles are equivalent. As in line with definition: in a traingle if the two angles are equivalent, then that traingle is referred to as a isoscele traingle.