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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.
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.
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.
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
solve for BD to get:
BD = sin(BAD) * AB
BD = .662620048 * 3.93 = 2.604096789 meters.
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.
Now that you are finished with all your calculations, you can round this to 5.4 square meters.
A picture of your triangle can be found at the following website:
Click on problem number 213743.
If it's not there when you look, wait 30 minutes and try again. It will be there.