SOLUTION: Obtain the area of a triangular plastic sheet whose sides are 3.93m and 4.15m if the angle between them is 41degrees 30'.

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Question 213743: Obtain the area of a triangular plastic sheet whose sides are 3.93m and 4.15m if the angle between them is 41degrees 30'.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
sides are 3.93m and 4.15m.
angle between them is 41 degrees 30 minutes.
area of a triangle is 1/2 base times height
you need to find the height of the triangle.
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label your triangle ABC.
A is the vertex of your angle.
B is the other end of the 3.93 meter side.
C is the other end of the 4.15 meter side.
draw a line from B to side AC intersecting with side AC at a right angle.
call that intersection D.
your triangle is now:
ABC plus BD intersecting with AC at point D.
your angle is angle A which is formed by sides AB and AD. The angle is otherwise known as angle BAD.
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you need to convert your angle into degrees.
angle BAD = 41 degrees 30 minutes.
30 minutes = 30/60 degrees = .5
add .5 to 41 degrees and your angle becomes 41.5 degrees.
angle BAD is now converted to degrees.
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you may find the length of side BD by taking the sine of angle BAD.
sine of angle BAD = opposite / hypotenuse.
BD = opposite
AB = hypotenuse
sin(BAD) = BD / AB
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solve for BD to get:
BD = sin(BAD) * AB
This becomes:
BD = .662620048 * 3.93 = 2.604096789 meters.
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you now have enough information to calculate the area of the triangle.
area of a triangle = (base * height)/2.
base of the triangle = AC = 4.15 meters.
height of the triangle = BD = 2.604096789 meters
area of the triangle = (AC * BD )/2 = (4.15 * 2.604096789)/2 = 5.403500838 meters.
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Now that you are finished with all your calculations, you can round this to 5.4 square meters.
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A picture of your triangle can be found at the following website:
http://theo.x10hosting.com/
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Click on problem number 213743.
If it's not there when you look, wait 30 minutes and try again. It will be there.
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