Question

the larger angle of a parallelogram is 126 degree. if its sides have lengths 30 cm and 36 cm, find the length of the shorter diagonal and it's area

Answer 1

use the law of the cosines on the triangles

Answer 2

if x is the shorter diagonal then:
x^2 = 30^2 + 36^2 - 2*30*36*cos(126)

Answer 3

can you work from there?

Answer 4

honestly i don't really have idea all about that ,, because i'm absent for 1 week because of some sort of reason :D

Answer 5

area is 0.5absinc for triangle so double the value
2* 0.5*30*36 *sin126
the use cosine rule a^2=b^2+c^2-2bc cosa
the diagonal is a and angle opposite is a so look at it and if you don't have the angle opposite work it out by 180-126 or use 126 if that is opposite then substitute

Answer 6

well^ did u get that O.o

Answer 7

my classmate told me what they study on that 1 week .. then i stock on the law of cosines because i can't really solve that problem hahaha

Answer 8

ahh ok well u can basically use the law of cosines: a^2 = b^2 + c^2 - 2bc cos(A)

Answer 9

so dats wut i did above

Answer 10

and u get x to equal 58.87 cm

Answer 11

which would be the length of the shorter diagonal

Answer 12

cosine rule a^2=b^2+c^2-2bc cosa
you need one angle lets say 126 and the two sides either side of the angle (b and C) so answer is a=sqrt (30^2 and 36^2-2*30*36*cos126) or if the shorter side is the other one it would be a=sqrt(30^2 and 36^2 - 2*30*36*cos(180-126)) depending which angle it is opposite

Answer 13

from the law of cosine

b^2=a62+c62-2accosB
36^2= a^2+30^2-2(a)(30)cos126degree
1296=a^2+(900)-2(a)(30)(-0.5877)
1296= a^2+900+35.26 a

the question is using quadratic function how can i get the a using 1296= a^2+900+35.26 a

Answer 14

why dont u rearrange it this way: x^2 = 30^2 + 36^2 - 2*30*36*cos(126)

Answer 15

put your fingers in a v shape like victory sign, put them on top of the diagram where the gap between your two fingers is on the diagonal you need now read the angle between your two fingers now use that angle it is either 126 or 180-126 the two fingers should be on top of your 30 and 36 which is the sides you need to use in the formula as I showed in the solution in either case you don't get quadratic equation if you choose the correct angle

Answer 16

your side on the first side of the equation is always the side opposite the angle. Pythagoras is a special case of cosine rule where angle is 90 cos90 is 0.