Question
in the figure ABCD is a parallelogram. AL is perpendicular to BC, AM is perpendicular to CD , AL = 4 cm and AM = 5 cm if BC =6.5 cm then find the value of CD
Answers
Reiny
Had to experiment until I got your figure correct, I think I got it
given: BC = AD = 6.5
angle B = angle D = Ø
in triangle AMD,
sinD = sinØ
= 5/6.5
D = appr 50.28° (I stored it in my calculator)
In triangle ABL
sinB = sinØ
= 4/AB
5/6.5 = 4/AB
5AB = 26
AB = 26/5 = 5.2
since CD = AB
CD = 5.2
At this point I realize I could have skipped all the above and just used the ratio of our two similar triangles and started with
5/6.5 = 4/AB
given: BC = AD = 6.5
angle B = angle D = Ø
in triangle AMD,
sinD = sinØ
= 5/6.5
D = appr 50.28° (I stored it in my calculator)
In triangle ABL
sinB = sinØ
= 4/AB
5/6.5 = 4/AB
5AB = 26
AB = 26/5 = 5.2
since CD = AB
CD = 5.2
At this point I realize I could have skipped all the above and just used the ratio of our two similar triangles and started with
5/6.5 = 4/AB