A "trig"cky situation

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  • So some trigonometry teacher named "Elaine Dria" wants a plot of land to build a house here at Sunnyside Acres...
  • So? What's the issue?
  • Here's where she wants the plot. The issue is that she's so crazy about teaching trig that she wants a triangular shaped plot!  How odd!
  • What? That is crazy!  How will we ever calculate the area of this triangular plot if we don't have the height?
  • We don't need the height, silly!  We just need two side lengths and the angle that connects the two.
  • side b (3 hm)
  • A (30)
  • side c (4 hm)
  • The equation to find the area of a triangle without needing the height is....A = .5(side b times side c) times Sine of A.....So by plugging our numbers into the equation, we get....A = .5(3 x 4)Sin30....Since 3 times 4 is 12, and half of 12 is 6, we simply have to multiply 6 by the sine of 30!
  • Ahhhhh this is so so so so so hard!!! What in the world is even a sine?  I can't do this!
  • Dude, quit throwing a temper tantrum.  Sine is just a trigonometric ratio.  In a right triangle, it is a ratio of the opposite leg to the angle and the hypotenuse.  But for here, you can just use a calculator.
  • So...I used my calculator and found that the sine of 30 degrees is .5, so multiplying that by 6 is 3..... I guess the area of our triangular plot is 3 hectometers squared????
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