Can anyone give me some idea how do I figure out the measure of DC? it doesn't seem possible to obtain the ideal answer by doing it without that. here the link below is the complete picture of this question, please reply with a considerate answer with explcit explaination. thanks pal.
http://img15.imagevenue.com/img.php?image=57713_DSC01506_122_745lo.JPG
2007-05-03 18:53:00 · 5 answers · asked by liangjizong22 1 in Science & Mathematics ➔ Mathematics
First find what the height of DH, the perpendicular from D to AB. You can get the real numbers from a graphing calculator or use google or some online calculator.
tan(angle) = opposite/hypotenuse
tan(73) = DH / 6 --> DH = 6 * tan(73)
tan(17) = AH / 6 --> AH = 6 * tan(17)
Area of the ADH triangle is: (length*height)/2 = AH*DH / 2 = (36*tan(73)*tan(17))/2
and the area of the trapezoid should be
2 * area(ADH) + square(DH)
2007-05-03 19:18:24 · answer #1 · answered by deque 2 · 0⤊ 0⤋
I don't have a calculator with me but here's a hint...
First you draw a line (DH) from D straight down to the line AB forming a triangle ADH. Angle A is 73 degrees and Angle H is 90 degrees (I wish I could draw it, I hope you get the idea). You know that AD is 6 so that means you have two angles and a side. With that you can find every angle and side of that triangle with the Sin Law which is:
a/SinA=h/SinH=d/SinD
(the letters are arbitrary) in this case:
a=line DH (side opposite to angle A)
h=line AD (side opposite to angle H) (in this case 6)
d=line AH (side opposite to angle D)
so using the Sin Law formula we can say that:
a/Sin73=6/Sin90
which is the same as a=6(Sin73)/Sin90
Once you get side a finding the rest of the sides of the triangle is easy. Once you know the sides of the triangle you can just break the shape up into four right angle triangles and solve the measurement of DC in the same way (I'm pretty sure if you break the shape into 4 right angle triangles they are all equal anyways)
Good luck!
2007-05-04 02:19:07 · answer #2 · answered by alexk 2 · 0⤊ 0⤋
since iso triangle & BAD = 73 degrees, drop a perpenduclar from D to AB - call it DH. Then ADH = 17. And DH = DC, so - DH = DC = 6 X cos(90-73) = 5.7378
2007-05-04 02:35:14 · answer #3 · answered by Anonymous · 0⤊ 0⤋
It's an isosceles trapezoid. Basically, if you took DC and added twice HA, you'd get AB. Using algebra, DC = AB - 2 * HA
2007-05-04 01:58:01 · answer #4 · answered by atmtarzy 2 · 0⤊ 0⤋
There is simply not enough information for a numerical solution. The best you can do is a formula for both area and perimeter.
2007-05-04 02:25:41 · answer #5 · answered by Helmut 7 · 0⤊ 0⤋