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The length of LN rounded to the nearest tenth is 2.70 and it can be evaluated by using the trignometry functions and rounding off rules to the nearest tenth.

Given :

[tex]\rm sin (20^\circ) = \dfrac{LN}{8}[/tex]

The length of LN rounded to the nearest tenth can be determine by using trignometry functions and rounding off rules to the nearest tenth.

Rounding off rules to the nearest tenth are as follows:

  • If the digit in unit place is in between 0 to 4 than replace it by zero.
  • If the unit place digit is in between 5 to 9 than replace unit place digit by 0 and increase the tens place digit by 1.

Now, to find the length of LN the given expression is further simplified.

[tex]\rm sin(20^\circ) = \dfrac{LN}{8}[/tex]

[tex]\rm LN = sin(20^\circ)\times 8[/tex]

[tex]\rm LN = 2.73[/tex]

Therefore, the length of LN rounded to the nearest tenth is 2.70.

For more information, refer the link given below:

https://brainly.com/question/24390851