1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Right Angle Trigonometry

  1. Dec 14, 2014 #1
    Problem was initially posted in a technical math section, so is missing the homework template.
    From a position 150 ft above the ground, an observer in a building measures angles of depression of 12° and 34° to the top and bottom, respectively, of a smaller building, as in the picture on the right. Use this to find the height h of the smaller building.

    I have found that the angle between the observer and the ground is 56°; however, when I use the tangent function to get the distance between the smaller building and the observer [150 tan(56)] I get the wrong answer and I do not understand why. The only solutions to this problem that I have found involve the law of sines, which has not been covered yet. If I knew the distance between the observer and the smaller building (let's call it x), then I would be able to construct a right triangle from the observing to above the smaller building, where the triangle would have acute angles 78 and 12 and a leg of length x; however, I would not know how to proceed from there.

    My questions are: why can I not use [150 tan(56)] to calculate x, how do I calculate x, and how do I find h from the triangle with leg x and angles 78 and 12.
     
    Last edited by a moderator: Dec 15, 2014
  2. jcsd
  3. Dec 14, 2014 #2

    Mark44

    Staff: Mentor

    A drawing would be very helpful.

    One thing I need to ask - is your calculator in degree mode?
     
  4. Dec 14, 2014 #3
    I did my best to draw it, and yes, my calculator is in degree mode. I used variables to represent any quantity that wasn't explicitly given to me by the problem. By the complement rule, I think theta is 56°; however, I get the wrong answer for x when I do [150 tan(56)]. It is apparently solvable without the law of sines as the book has not covered that idea yet.

    I believe that A is 90° and that B is 78°. I want to find the variable "h," which is the height of the small building.
     

    Attached Files:

  5. Dec 15, 2014 #4

    Mark44

    Staff: Mentor

    Your equation of x = 150 tan(56°) is fine. I did it another way, but the two ways are equivalent. All you need is another equation that involves x and h.

    In your drawing, extend the line segment of length h all the way to the top so that you have a rectangle that is 150' by x'. Using the 34° you can use the dimensions of the triangle whose acute angle is 34° - that's your second equation. You don't need the Law of Sines or the Law of Cosines - just some ordinary right triangle trig.

    BTW, this is a homework problem, so I am moving it to the Homework & Coursework sections, which is where problems of this sort should be posted.
     
  6. Dec 15, 2014 #5
    Oh, it looks like I forgot to subtract h from 150! The answer is then 103. Thank you for the advice!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Right Angle Trigonometry
  1. Find Trigonometry angle (Replies: 11)

Loading...