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November 20th, 2011, 06:59 AM   #1
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Simple, not so simple question about areas of triangles

I keep getting mixed answers from tutors when asking this question, so if someone could please help me out it would help tremendously. I am wondering how to find the area of a non right triangle, given the lengths of 2 sides and the angle in between them. I know the formula 1/2(b)(h)(sinx)

I wish I could draw the triangle to show why I am so confused, but apparently my definition of the word "height" and other people's is two different things.

The triangle I have is triangle DEF

DE = 7 feet
EF = 5 feet
and angle E = 135 degrees

I was told to simply plug the numbers into the formula, which would be: 1/2(7)(5)(sin 135 degrees -- ?2/2) which calculates to 32?2/4

this is assuming that the height is 5 feet. The only problem I have with that assumption is that the side EF is not a vertical line, it is actually pointing out 45 degrees, therefore it would seem to me that the actual height is the distance between angle F and the base. I hope that I explained this clearly enough so that someone can understand what I am asking and help me out with this, because I really need to get this figured out ASAP. Thanks to whoever can help me.
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November 20th, 2011, 08:14 AM   #2
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Re: Simple, not so simple question about areas of triangles

Make a diagram. The height is 5 * sin(135) (this follows from the definition of the sine), assuming the base is DE.

sin(180 - x) = sin(x), so sin(135) = sin(180 - 135) = sin(45), if you're wondering why a 45 angle isn't used.
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