Length of AB is 18
Step-by-step explanation:
- Step 1: Find length of AB when AC = 9√3 and ∠B = 60°. Use trigonometric ratio sine.
sin 60 = opposite side/hypotenuse = 9√3/x
x = 9√3/sin 60
= 9√3/√3/2 = 9√3 × 2/√3 (∵ a ÷ b = a×1/b)
= 18
In this item, it is unfortunate that a figure, drawing, or illustration is not given. To be able to answer this, it is assumed that these segments are collinear. Points L, M, and N are collinear, and that L lies between MN.
The length of the whole segment MN is the sum of the length of the subsegments, LN and LM. This can be mathematically expressed,
LN + LM = MN
We are given with the lengths of the smalller segments and substituting the known values,
MN = 54 + 31
MN = 85
<em>ANSWER: MN = 85</em>
Rectangular parallelepiped, right rectangular prism)
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