Sooo...the lengths of the diagnals of a parallelogram are 20 inches and 30 inches. The diagnols intersect at an angle of 35 degrees. Find the lengths of the paralellogram's sides (HInt: diagnols of a parallelogram bisect one another!)
2006-12-14 20:48:36 · 6 answers · asked by nietzsche 1 in Science & Mathematics ➔ Mathematics
Draw a parallelogram. Draw the two diagonals, which will give you a big "x" in your parallelogram. Use the hint to find out the lengths of the four bars of this "x" (e.g. if one diagonal is 20 inches in length, then half of it would be...?). They intersect at a 35 degree angle, so mark one of the inner angles next to the intersection as being "35 degrees". To find the other three angles, use the opposite angle rule (the angle on the other side of the 35 degree angle would be 35 degrees too) and the other two angles would just be 180-35.
So now you have your parallelogram broken up into 4 triangles. Two of them have 10 and 15 for side lengths with an angle of 35 in between. The other two triangles have 10 and 15 for the side lengths and an angle of 145 in between. Use the law of cosines on each of these to find the third side, which will each be one of the sides of the parallelogram.
2006-12-14 21:02:18 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Let the lengths of two opposing sides be a and the other two sides b. Let the side b be opposite the 35° angle and the side a opposite the (180° - 35°) = 145° angle.
Use the law of cosines. The three sides of the triangle are 20/2, 30/2, and b. Namely, 10, 15, and b.
b^2 = 10^2 + 15^2 - 2*10*15 cos 35°
b^2 = = 100 + 225 - 300 cos 35°
b^2 = 325 - 300 cos 35°
b = sqrt(325 - 300 cos 35°) = 8.9024933
a2 = 10^2 + 15^2 - 2*10*15 cos 145°
a2 = = 100 + 225 - 300 cos 145°
a2 = 325 - 300 cos 145°
a = sqrt(325 - 300 cos 145°) = 23.890283
So the lengths of the parallelograms side consist of two sets of opposite side of length:
8.9024933 inches and
23.890283 inches
2006-12-14 21:04:35 · answer #2 · answered by Northstar 7 · 0⤊ 0⤋
it's really simple... You just have to use the law of sines...
Calculate the side of one of the "triangles" and then divide it to the sin of 36. then that would be equal to the length of the other side divided by the sine of its respective angle....
2006-12-14 21:05:29 · answer #3 · answered by BJ 2 · 0⤊ 0⤋
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2016-10-14 23:53:46 · answer #4 · answered by ? 4 · 0⤊ 0⤋
One is 23.89 inch while the other is 8.9 inch.
2006-12-14 21:01:10 · answer #5 · answered by Elicasel 3 · 0⤊ 0⤋
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2006-12-14 20:52:47 · answer #6 · answered by Sweetheart88 5 · 0⤊ 1⤋