[tex]\huge\boxed{6.5\ \text{feet}}[/tex]
Since all of the angles of a triangle add up to [tex]180^{\circ}[/tex], we can use that to find [tex]\angle L[/tex].
[tex]90+13+\angle L=180[/tex]
[tex]103+\angle L=180[/tex]
[tex]\angle L=77[/tex]
Using SOHCAHTOA, we know that the sine of an angle is equal to the opposite side's length divided by the hypotenuse's length.
[tex]\sin(\angle L)=\overline{MN}\div\overline{LM}[/tex]
[tex]\sin(77)=\overline{MN}\div6.5[/tex]
Find [tex]\sin(77)[/tex] and round to the nearest tenth.
[tex]1\approx\overline{MN}\div6.5[/tex]
Multiply both sides by [tex]6.5[/tex].
[tex]\boxed{6.5}\approx\overline{MN}[/tex]
The length of the side of MN in the triangle LMN to the nearest tenth of a foot is 6.5 feet.
we have given that,
In ΔLMN, the measure of ∠N=90°, the measure of ∠M=13°, and LM = 6.5 feet.
The sum of the all angle in a triangle is 180 degrees.
Therefore L+M+N=180 degrees.
L+13+90=180
L=77 degrees
We know that the sine of an angle is equal to the opposite side's length divided by the hypotenuse's length.
[tex]sin(L)=\frac{MN}{LM} \\\\\sin(77)=\frac{MN}{6.5} \\\\\\MN=6.5feet[/tex]
Therefore, The length of the side of MN to the nearest tenth of a foot is 6.5 feet.
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