x = 46.77
Step-by-step explanation:
To find the missing length, we need to partition the trapezoid
Using an illustration:
So first, we solve for y :
adjacent = base = y
hypotenuse = 24
angle = 45 degree
using cosine ratio:
cos 45 = adjacent/hypotenuse
sin 45 = y/24
cross multiply:
24×cos45 = y
y = 24(0.7071)
y = 16.97
Now we solve for z:
Adjacent angles of a trapezoid are supplementary.
The red arrow are the adjacent angles
120 + the adjacent angle at the base = 180 degree
the adjacent angle at the base = 180 -120
the adjacent angle at the base = 60 degree
using sine rule, we find the height
sin45 = opposite/hypotenuse
sin45 = height/24
h = 24×sin45 = 24(0.7071)
h = height = 16.9704
since we have gotten the height, we apply tangent ratio to get z:
tan60 = opposite/adjacent = height/adjacent
tan60 = 16.9704/z
z × tan60 = 16.9704
z = 16.9704/tan60
z = 16.9704/1.7321
z = 9.80
The length of the missing side of the trapezoid = x
x = y + w + z
w = 20 (it is parallel with base on top)
x = 16.97 + 20 + 9.8
x = 46.77