anonymous
  • anonymous
Find the area of the trapezoidal cross-section of the irrigation canal shown below. Your answer will be in terms of h, w, and θ. http://www.webassign.net/hgmcalc5/1-5-049.jpg
Mathematics
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SOLVED
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chestercat
  • chestercat
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NoelGreco
  • NoelGreco
|dw:1346472458903:dw| Can you calculate p from some trig function of theta ("th" is theta in drawing)
anonymous
  • anonymous
1/2*p*h=area?
NoelGreco
  • NoelGreco
Yeah, but we really need to use p temporarily. First of all do you see how I got the theta near the p?

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anonymous
  • anonymous
its a complmentary angle? sorry im totally lost
NoelGreco
  • NoelGreco
No, actually, it's congruent to the theta given in the problem because alternate interior angles of transversals and parallel lines are congruent. Does that ring any bells?
anonymous
  • anonymous
kindof but i dont know why you would do that
NoelGreco
  • NoelGreco
Well, if I knew an expression for p, I could say that the long base of the trapezoid was w + 2p, the other base is w, and we have h. That's all you need for the area of a trapezoid.
NoelGreco
  • NoelGreco
Isn't \[\tan \theta = \frac{ h }{ p}\]
anonymous
  • anonymous
yeah so what would the area be?
anonymous
  • anonymous
tan(theta)*p/h
anonymous
  • anonymous
@NoelGreco

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