SOLUTION: Hi, this is a trig word problem involving height of buildings and I want it soved by tomorrow (12/14/2009, PST) by the latest. Here it is: The window on the fourth floor of a bu

Algebra ->  Trigonometry-basics -> SOLUTION: Hi, this is a trig word problem involving height of buildings and I want it soved by tomorrow (12/14/2009, PST) by the latest. Here it is: The window on the fourth floor of a bu      Log On


   

Question 249561: Hi, this is a trig word problem involving height of buildings and I want it soved by tomorrow (12/14/2009, PST) by the latest. Here it is:
The window on the fourth floor of a building is 30 m above the ground. From the window, the angle of depression to the base of a nearby building is 31 degrees and the angle of elevation to the top of the building nearby is 40 degrees. How tall is the nearby building to the nearest metre?
I just want to know how to draw out the problem. Your help is most appreciated, thanks!
~S.N.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
here's your diagram.

http://theo.x10hosting.com/problems/249561.html

you draw a line parallel to the ground from the window to the opposite building.

that would be line AB

you draw a line from the windoiw to the base of the building next door.

that would be line AC.

you draw a line from the window to the top of the building next door.

that would be line AE.

your angle of depression is angle BAC.

your angle of elevation is angle EAB.

line AD is 30 feet.

so is line BC because it's on the opposite end of the rectangle that you drew which is rectangle ABCD.

you need to find the length of line AB.

use tan(31) = BC/AB go get line AB.

use tan(40) = EB/AB to get line EB.

height of building is line EC which is the sum of lines EB and BC.

any further questions, send me an email.

i'll be checking in the morning.