Question

in the figure shown, point m is the mid - point of $overline{rs}$ and the length of $overline{qr}$ is given in units. which value best represents the length, in units, of $overline{rm}$? a. 41.6 b. 24.0 c. 20.8 d. 12.0

Explanation:

Step1: Use cosine - function in right - triangle

In right - triangle $QSR$, $\cos R=\frac{RS}{QR}$. Given $\angle R = 60^{\circ}$ and $QR = 48$. Since $\cos60^{\circ}=\frac{1}{2}$, we have $RS=QR\times\cos R=48\times\frac{1}{2}=24$.

Step2: Use mid - point property

Since $M$ is the mid - point of $RS$, then $RM=\frac{1}{2}RS$. Substituting $RS = 24$ into the formula, we get $RM=\frac{24}{2}=12$.

Answer:

D. 12.0