Question

name: yolissa a

1. determine the length of mn to the nearest tenth of a centimetre.

a. 36.9 cm
b. 41.4 cm
c. 8.5 cm

Explanation:

Step1: Identify the trigonometric relation

In right - triangle $LMN$ with right - angle at $M$, we know the hypotenuse $LN = 18.8$ cm and the angle $\angle N=63^{\circ}$, and we want to find the side $MN$. We use the cosine function since $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, where $\theta = 63^{\circ}$ and the adjacent side to $\angle N$ is $MN$ and the hypotenuse is $LN$.
$\cos(N)=\frac{MN}{LN}$

Step2: Substitute the known values

We know that $N = 63^{\circ}$ and $LN=18.8$ cm. So, $MN = LN\times\cos(N)$.
$MN=18.8\times\cos(63^{\circ})$
Since $\cos(63^{\circ})\approx0.454$, then $MN = 18.8\times0.454$.
$MN=18.8\times0.454 = 8.5352\approx8.5$ cm

Answer:

C. 8.5 cm