Results 1 to 6 of 6

Math Help - Find Angle Theta

  1. #1
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    Find Angle Theta

    A 10-meter telephone pole casts a shadow directly down a slope when the angle of elevation of the sun is 42 degrees.
    Find theta, the angle of elevation of the ground.

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,492
    Thanks
    1393
    Quote Originally Posted by magentarita View Post
    A 10-meter telephone pole casts a shadow directly down a slope when the angle of elevation of the sun is 42 degrees.
    Find theta, the angle of elevation of the ground.
    Remember that the sum of three angles in a triangle is 180^{\circ}.

    Provided that the telephone pole is perpendicular to the ground (as all are), then 90^{\circ} + 42^{\circ} + \theta ^{\circ} = 180^{\circ}.

    132^{\circ} + \theta ^{\circ} = 180^{\circ}

    \theta ^{\circ} = 48^{\circ}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    but...

    Quote Originally Posted by Prove It View Post
    Remember that the sum of three angles in a triangle is 180^{\circ}.

    Provided that the telephone pole is perpendicular to the ground (as all are), then 90^{\circ} + 42^{\circ} + \theta ^{\circ} = 180^{\circ}.

    132^{\circ} + \theta ^{\circ} = 180^{\circ}

    \theta ^{\circ} = 48^{\circ}.
    But this is trigonometry not geometry, right? I was told that we must take the inverse if the trig function to find theta.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Jan 2009
    Posts
    145
    Remember that the sum of three angles in a triangle is .

    Provided that the telephone pole is perpendicular to the ground (as all are), then .



    .
    I believe the mistaken assumption was that the angle of elevation was angle between the top of the telephone poll and the shadow being cast. The angle of elevation for the sun is going to be the angle between the ground and the sun. Further, the telephone poll appears to be casting a shadow down a hill, not across a plane. The question is asking for the angle of elevation for the hill.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by Math Major View Post
    I believe the mistaken assumption was that the angle of elevation was angle between the top of the telephone poll and the shadow being cast. The angle of elevation for the sun is going to be the angle between the ground and the sun. Further, the telephone poll appears to be casting a shadow down a hill, not across a plane. The question is asking for the angle of elevation for the hill.
    A diagram would be nice. It would appear that the pole would not be perpendicular to the ground since it is on a slope. I've attached a sketch, but there's not enough info to solve for \theta, if that is where \theta is.
    Attached Thumbnails Attached Thumbnails Find Angle Theta-angle.jpg  
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    Yes....

    Quote Originally Posted by masters View Post
    A diagram would be nice. It would appear that the pole would not be perpendicular to the ground since it is on a slope. I've attached a sketch, but there's not enough info to solve for \theta, if that is where \theta is.
    Nice picture but I think there is something missing from this question.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 29th 2010, 06:38 AM
  2. Replies: 1
    Last Post: September 11th 2009, 06:46 AM
  3. How to find the measure of angle theta
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 19th 2009, 06:33 PM
  4. Replies: 3
    Last Post: February 6th 2009, 03:19 PM
  5. Replies: 1
    Last Post: January 23rd 2009, 09:53 AM

Search Tags


/mathhelpforum @mathhelpforum