Results 1 to 3 of 3

Math Help - Right Triangle Trig word problem

  1. #1
    Junior Member
    Joined
    Sep 2008
    From
    Canada
    Posts
    42

    Right Triangle Trig word problem

    I'm stuck on this...sorry, there's a diagram I dont' have time to scan, but hopefully it is clear enough:

    "A flagpole is located at the edge of a sheer 50ft cliff at the bank of a river of width 40 feet. An observer on the opposite side of the river measures an angle of 9 degrees between her line of sight to the top of the flagpole and her line of sight to the top of the cliff. Find the height of the flagpole."

    So we know that the cliff is 50feet, but we don't know what the flagpole is so that would be 50+x correct?
    And there's a right-angle with the base of 40 feet and height of 50 feet, so the hypotenuse would be 60 feet I believe.
    But I don't think that helps me. Very confused...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    Quote Originally Posted by tiar View Post
    I'm stuck on this...sorry, there's a diagram I dont' have time to scan, but hopefully it is clear enough:

    "A flagpole is located at the edge of a sheer 50ft cliff at the bank of a river of width 40 feet. An observer on the opposite side of the river measures an angle of 9 degrees between her line of sight to the top of the flagpole and her line of sight to the top of the cliff. Find the height of the flagpole."

    So we know that the cliff is 50feet, but we don't know what the flagpole is so that would be 50+x correct?
    And there's a right-angle with the base of 40 feet and height of 50 feet, so the hypotenuse would be 60 feet I believe.
    But I don't think that helps me. Very confused...
    You don't actually need to find the length of the hypotenuse. If you assume the observer has no height, then the angle between her line of sight to the base of the cliff to the top of the cliff is arctan(50/40) degrees, and the angle between her line of sight to the base of the cliff to the top of the flagpole is [arctan(50/40) + 9] degrees. Can you figure it out after calculating that angle?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,682
    Thanks
    614
    Hello, tiar!

    A flagpole is located at the edge of a sheer 50ft cliff at the bank of a river 40 feet wide.
    An observer on the opposite side of the river measures an angle of 9 degrees between
    her line of sight to the top of the flagpole and her line of sight to the top of the cliff.
    Find the height of the flagpole.
    Code:
                              o A
                            * |
                          *   |
                        *     | h
                      *       |
                    *         o B
                  *       *   |
                * 9  *       |
              *   *           | 50
            * *  θ            |
        P o - - - - - - - - - o C
                    40

    The flagpole is h = AB.
    The cliff is BC = 50.
    The observer is at P\!:\;\;PC = 40.
    \angle APB = 9^o.
    Let \theta = \angle BPC.


    In right triangle BCP\!:\;\tan\theta = \tfrac{50}{40} = \tfrac{5}{4}


    In right triangle ACP\!:\;\;\tan(\theta + 9^o) \:=\:\frac{h+50}{40}\;\;{\color{blue}[1]}

    . . Note that: . \tan(\theta + 9^o) \:=\:\frac{\tan\theta + \tan9^o}{1-\tan\theta\tan9^o} \;=\;\frac{\frac{5}{4} + \tan9^o}{1 - \frac{5}{4}\tan9^o} . = \:\frac{5+4\tan9^o}{4-5\tan9^o}

    Substitute into [1]: . \frac{5+\tan9^o}{4-5\tan9^o} \;=\;\frac{h+50}{40} \quad\Rightarrow\quad h \;=\;40\cdot\frac{5 + 4\tan9^o}{4-5\tan9^o} - 50


    Therefore: . h \;=\;20.24190952 \;\approx\;20.24\text{ ft}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig word problem - solving a trig equation.
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: March 14th 2011, 07:07 AM
  2. Trig triangle word problem
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 17th 2010, 10:46 PM
  3. Triangle word problem
    Posted in the Geometry Forum
    Replies: 1
    Last Post: March 7th 2010, 12:14 PM
  4. A Right Triangle Word Problem
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: July 16th 2009, 11:10 PM
  5. triangle word problem
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 12th 2008, 06:44 PM

Search Tags


/mathhelpforum @mathhelpforum