Results 1 to 14 of 14

Math Help - Find the Angle

  1. #1
    Member
    Joined
    Mar 2012
    Posts
    169

    Find the Angle

    Tangents AB and AC are drawn to a circle through a point A on the outside of the circle, which has center O. If AO = 36.72 and the radius of the circle is 15.84, find the angle BAC made by the two tangents.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    17,283
    Thanks
    2139

    Re: Find the Angle

    Look at AOB and AOC. Those are identical right triangles in which you know the hypotenuse (AO) and one leg, OB in one and OC in the other, radii of the circle.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Mar 2012
    Posts
    169

    Re: Find the Angle

    Can you draw a Picture?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,962
    Thanks
    798

    Re: Find the Angle

    Draw a circle with a point A above the circle. Draw a line from A so that it just touches the upper left side of the circle, then draw a line from A so it just touches the upper right side of the circle. There is your diagram. The points of intersection are B and C.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    910
    Thanks
    376

    Re: Find the Angle

    Here's my advice. Download any one of numerous free dynamic geometry programs. Spend a little time in learning to use it. Then draw your own pictures. Besides being able to produce accurate diagrams, the construction of a given figure generally forces you to think about the geometry/trigonometry required. It took me all of 10 minutes to draw the annotated figure.

    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Mar 2012
    Posts
    169

    Re: Find the Angle

    Why didn't you choose B and C to be in the middle of the circle? I mean Left and right.
    Last edited by joshuaa; July 29th 2014 at 06:49 AM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,962
    Thanks
    798

    Re: Find the Angle

    Quote Originally Posted by joshuaa View Post
    Why didn't you choose B and C to be in the middle of the circle? I mean Left and right.
    Because tangent lines intersect the outside of a circle, not the middle of it.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member
    Joined
    Mar 2012
    Posts
    169

    Re: Find the Angle

    No. I mean that why COB is not a straight Line!
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,962
    Thanks
    798

    Re: Find the Angle

    Quote Originally Posted by joshuaa View Post
    No. I mean that why COB is not a straight Line!
    Better question: Why would you think COB would be a straight line? There is no reason to think it would be, and you can easily prove that it is not.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Member
    Joined
    Mar 2012
    Posts
    169

    Re: Find the Angle

    I would think that COB is a straight line because it is easier to draw a Triangle when I connect them to A.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,962
    Thanks
    798

    Re: Find the Angle

    Quote Originally Posted by joshuaa View Post
    I would think that COB is a straight line because it is easier to draw a Triangle when I connect them to A.
    You can draw a straight line from A to B, but it will not pass through the center of the circle O. I'm not sure what you are missing here. This seems extremely straightforward.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Member
    Joined
    Mar 2012
    Posts
    169

    Re: Find the Angle

    Thanks a Lot SlipEternal. It is better to go on with other Problems after I have got the idea of this problem.
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Banned
    Joined
    Aug 2014
    From
    new york
    Posts
    2

    Re: Find the Angle

    It's like a rectangular box which is open and light can go down through this box and not only that but the inside surfaces have this box I rock mirror their silver their Ripped Muscle X shiny so what happens when like those in this box it kind of ricochets off both sides in zigzags down through this sum up open in finally tell hits the sensors that the a lobster can see it's a very different type ova optics than what we have today but itís have interest to the space-age now um stars give of many more kinds have liked and we can see there's more light than meets the eye at hereís not only visible light but there's gamma rays there's infrared light and there's X-rays that stars give off and we can measure those X-rays we can learn a lot about.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    MHF Contributor

    Joined
    Apr 2005
    Posts
    17,283
    Thanks
    2139

    Re: Find the Angle

    Quote Originally Posted by JordanTPreiss View Post
    It's like a rectangular box which is open and light can go down through this box and not only that but the inside surfaces have this box I rock mirror their silver their Ripped Muscle X shiny so what happens when like those in this box it kind of ricochets off both sides in zigzags down through this sum up open in finally tell hits the sensors that the a lobster can see it's a very different type ova optics than what we have today but it’s have interest to the space-age now um stars give of many more kinds have liked and we can see there's more light than meets the eye at here’s not only visible light but there's gamma rays there's infrared light and there's X-rays that stars give off and we can measure those X-rays we can learn a lot about.
    You seem to have forgotten to include the commercial link (which was probably supposed to be at "Ripped Muscle X"). You won't get paid for this one!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How can i find the angle X
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: February 9th 2013, 11:49 PM
  2. Replies: 1
    Last Post: April 4th 2011, 11:36 AM
  3. Find the angle ?
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 12th 2009, 03:37 PM
  4. Replies: 3
    Last Post: April 16th 2009, 08:45 AM
  5. find the angle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: June 20th 2007, 06:07 PM

Search Tags


/mathhelpforum @mathhelpforum