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Calculate the surface and the angle of the figure below.

  1. Nov 17, 2012 #1
    1. The problem statement, all variables and given/known data

    http://ima.cs-gamers.com.ar//images/490matjhs.jpg [Broken]

    I have to calculate the surface from the object and the angle alpha.

    2. Relevant equations

    [itex]A_{triangle} = \frac{b * h}{2} [/itex]

    [itex] \frac{a}{\sin \alpha_1} = \frac{b}{\sin \alpha_2} [/itex]

    Pythagorean Theorem

    3. The attempt at a solution

    I have calculated from differents methods, one with one rectangle and triangle. And the other form with dividing the object with two triangles.

    Dividing the object in two triangles thus leaving:

    The triangle with base (640) Can be that the angles of this triangle are 90 , 45 and 45?

    Because if they are well the height gives a value of I 640, which in the drawing does not correspond

    Help please
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 17, 2012 #2

    Mark44

    Staff: Mentor

    This is the simpler way, with a right triangle on the left and a rectangle on the right. It's very easy to get one of the legs of the right triangle. A little right triangle trig will then get you the side opposite the angle α.
     
    Last edited by a moderator: May 6, 2017
  4. Nov 18, 2012 #3
    I have done the following:

    [itex] \frac{500}{\sin 90º} = \frac{400}{\sin \beta} \to \beta = 53, 13º [/itex]

    [itex] 90º + 53,13º + \alpha = 180º \to \alpha = 36,87º[/itex]

    [itex] \sin 36,87º = \frac{h}{500} \to h = 300 [/itex]

    [itex] A_{triangle} = \frac{b*h}{2} = \frac{400 \cdot 300}{2} = 60000m^2 [/itex]

    [itex] A_{rectangle} = a * h = 640 * 300 = 192000 m^2 [/itex]

    [itex] A_T = 252000m^2[/itex]

    Is that correct?
     
    Last edited: Nov 18, 2012
  5. Nov 18, 2012 #4

    Mark44

    Staff: Mentor

    Looks good.

    You could have saved yourself some work by noting that the triangle is a right triangle. You know the base (400 m.) and the hypotenuse (500 m.), so cos(α) = 400/500 = 4/5 ##\Rightarrow ## α = cos-1(4/5) ≈ 36.87°.
     
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