Question

In ΔLMN, the measure of ∠N=90°, the measure of ∠M=13°, and LM = 6.5 feet. Find the length of MN to the nearest tenth of a foot.

Answer 1

Answer:

Step-by-step explanation:

\tan 16=\frac{x}{65}

tan16= 65x

65\tan 16=x

65tan16=x

x=18.6385≈18.6 feet

Answer 2

$\huge\boxed{6.5\ \text{feet}}$

Since all of the angles of a triangle add up to $180^{\circ}$, we can use that to find $\angle L$.

$90+13+\angle L=180$

$103+\angle L=180$

$\angle L=77$

Using SOHCAHTOA, we know that the sine of an angle is equal to the opposite side's length divided by the hypotenuse's length.

$\sin(\angle L)=\overline{MN}\div\overline{LM}$

$\sin(77)=\overline{MN}\div6.5$

Find $\sin(77)$ and round to the nearest tenth.

$1\approx\overline{MN}\div6.5$

Multiply both sides by $6.5$.

$\boxed{6.5}\approx\overline{MN}$