Results 1 to 3 of 3

Math Help - sine rule

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    20

    Post sine rule

    using the sine rule solve the following triangles DEF and find their areas
    d=17cm f=22cm F=26*
    could anyone please show me how to do this example so i could do the others
    tha
    nks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,903
    Thanks
    329
    Awards
    1
    Quote Originally Posted by jim49990 View Post
    using the sine rule solve the following triangles DEF and find their areas
    d=17cm f=22cm F=26*
    could anyone please show me how to do this example so i could do the others
    tha
    nks
    The Law of Sines is:
    \frac{d}{sin(D)} = \frac{e}{sin(E)} = \frac{f}{sin(F)}

    So for sides d and f:
    \frac{17}{sin(D)} = \frac{22}{sin(26)}

    sin(D) = \frac{17 \cdot sin(26)}{22} = 0.338741

    So D = 19.8^o. Now, D could merely be the reference angle, so it is possible that D = 180^o - 19.8^o = 160.2^o except that the sum of the interior angles in any triangle is 180 degrees. If D were 160.2 degrees then angle D plus angle F accounts for more than 180 degrees not even counting angle E. So angle D must be 19.8 degrees.

    So we know two angles in the triangle and as I said above we know that the sum of the interior angles of a triangle is 180 degrees. So for angle E:
    E = 180 - D - F = 180^o - 19.8^o - 26^o = 134.2^o

    Employing the Law of Sines for e and f:
    \frac{e}{sin(134.2)} = \frac{22}{sin(26)}

    e = \frac{22 \cdot sin(134.2)}{sin(26)} = 35.9788

    So side e is about 36.0 cm in length.

    There are various ways to get the area of the triangle. This is Heron's formula:
    A = \sqrt{s(s-d)(s-e)(s-f)} where s = \frac{d+e+f}{2} (Called the "semi-perimeter.")

    So
    s = \frac{17 + 36 + 22}{2} = 37.4894 (I am using the unrounded expression for e.)

    A = \sqrt{37.4894 (37.4894 - 17)(37.4894 - 36)(37.4894 - 22)} = 134.063

    So the area of the triangle is about 134.1 \, cm^2.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,719
    Thanks
    634
    Hello, Jim!

    Using the Sine Rule, solve triangle D{E}F and find its area.
    . . d = 17\text{ cm, } f = 22\text{ cm, }F = 26^o

    Dan did an excellent job in solving the triangle.

    Here's another way to find its area.
    . . \text{Area } = \:\frac{1}{2}bc\sin A

    One-half the product of two sides and the sine of the included angle.


    Since we know: . d = 17,\:f = 22,\:E = 134.2^o

    . . we have: . A \:=\:\frac{1}{2}(17)(22)\sin134.2^o \:=\:134.0622836 \:\approx\:134.1 cm².

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sine Rule q
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 16th 2009, 05:25 PM
  2. Sine rule...
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 22nd 2009, 03:46 PM
  3. Sine rule!
    Posted in the Geometry Forum
    Replies: 2
    Last Post: May 13th 2009, 01:40 PM
  4. sine rule
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: March 13th 2009, 09:12 PM
  5. The Sine Rule
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 31st 2008, 09:03 PM

Search Tags


/mathhelpforum @mathhelpforum