Results 1 to 5 of 5

Math Help - Angle C

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

    Angle C

    In
    ABC, if AC = 12, BC = 11, and measure of angle A = 30 degrees, angle C could be

    (1) an obtuse angle, only
    (2) an acute angle, only
    (3) a right angle, only

    (4) either an obtuse angle or an acute angle
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,992
    Thanks
    1129
    Quote Originally Posted by magentarita View Post
    In
    ABC, if AC = 12, BC = 11, and measure of angle A = 30 degrees, angle C could be

    (1) an obtuse angle, only
    (2) an acute angle, only
    (3) a right angle, only

    (4) either an obtuse angle or an acute angle
    (4) What you written makes no restriction on angle C at all.
    Follow Math Help Forum on Facebook and Google+

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

    ok but...........

    Quote Originally Posted by HallsofIvy View Post
    (4) What you written makes no restriction on angle C at all.
    I understand the answer is (4) but why?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,992
    Thanks
    1129
    Draw a picture! Draw line segment AC with length 12, angle A of 30 degrees- that is draw a ray without end starting at A and at 30 degrees. At the other end you know CB has length 11 but you don't know its direction so use compasses to strike an arc with radius 11. Where does it cross the ray you drew?

    There are three possiblities- if the radius were too short it wouldn't cross at all and there would be no triangle at all. With "11" and "12" that doesn't happen here. If this happened to be a right triangle, it would be just tangent to the ray. That doesn't happen here- there is no right triangle with angle 30, opposite leg 11 and hypotenuse 12: sin(30) is NOT 11/12.

    What happens here is that the arc of radius 11 crosses that ray twice. There are two possible triangles, one with an acute angle at B, the other with an obtuse angle at B.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Jul 2008
    From
    NYC
    Posts
    1,489

    ok.............

    Quote Originally Posted by HallsofIvy View Post
    Draw a picture! Draw line segment AC with length 12, angle A of 30 degrees- that is draw a ray without end starting at A and at 30 degrees. At the other end you know CB has length 11 but you don't know its direction so use compasses to strike an arc with radius 11. Where does it cross the ray you drew?

    There are three possiblities- if the radius were too short it wouldn't cross at all and there would be no triangle at all. With "11" and "12" that doesn't happen here. If this happened to be a right triangle, it would be just tangent to the ray. That doesn't happen here- there is no right triangle with angle 30, opposite leg 11 and hypotenuse 12: sin(30) is NOT 11/12.

    What happens here is that the arc of radius 11 crosses that ray twice. There are two possible triangles, one with an acute angle at B, the other with an obtuse angle at B.
    I thank you for the detailed reply.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: March 1st 2010, 09:53 AM
  2. Simplify the Expression (Double-Angle or Half-Angle)
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 3rd 2009, 03:38 PM
  3. Replies: 1
    Last Post: September 11th 2009, 06:46 AM
  4. Replies: 2
    Last Post: March 28th 2009, 02:18 PM
  5. Replies: 2
    Last Post: February 15th 2007, 10:16 PM

Search Tags


/mathhelpforum @mathhelpforum