If line segment ab measures approximately 8.6 units and is considered the base of parallelogram abcd, what is the approximate corresponding height of the parallelogram? round to the nearest tenth.3.7 units4.1 units4.8 units5.6 units

The correct option is 4.8 units

Step-by-step explanation:

Look at the attached picture.

AB = 8.6  

Coordinates of A(1, 3), B(8, 8), C(12, 5) and D(5, 0)

Now find the angle between AB and AD to find the length of AE which is the length of parallelogram.

tanθ = m(AB)-m(AD)/1+m(AB)m(AD)

Slope of mAB = y2-y1/x2-x1

Slope of mAB = 8-3/8-1

Slope of mAB = 5/7

Slope of mAD = 0-3/5-1 = -3/4

tanθ = 5/7 - (-3/4)/ 1+(5/7)(-3/4)

tanθ = 5/7+3/4 / 1+(-15/28)

tanθ = 20+21/28 /1 - 15/28

tanθ = 41/28 / 28-15/28

tanθ = 41/28 /13/28

Both the denominators will be cancelled out by each other.

tanθ = 41/13 = 3.154

θ = tan^-1 (3.154) = 72.41 degree

Now in right angle triangle ABE  

sin72.41° = DE/5

.95324 = DE/5

DE =  5×4.7662 = 4.8 units

Thus the correct option is 4.8 units