Answer:
The distance between the Supermarket and the bank is 854 meters
The distance between Ivy’s house and the Supermarket is 1,014 meters
Explanation:
We were given the following information:
Pont A represents Ivy's house
Point B represents the Supermarket
Point C represents the Bank
[tex]\begin{gathered} m\angle A=32^{\circ} \\ AB=c=? \\ BC=a=? \\ m\angle B=109^{\circ} \\ AC=b=1,523m \\ m\angle C=180-(109+32)=180-141=39^{\circ} \\ m\angle C=39^{\circ} \end{gathered}[/tex]We were given 2 known angles and 1 known side. We will thus solve using Sine Rule as shown below:
[tex]\begin{gathered} \frac{Sin(A)}{a}=\frac{Sin(B)}{b}=\frac{Sin(C)}{c} \\ \frac{Sin(32^{\circ})}{a}=\frac{Sin(109^{\circ})}{1,523} \\ \text{Cross multiply, we have:} \\ a\times Sin(109^{\circ})=1,523\times Sin(32^{\circ}) \\ a=\frac{1,523\times Sin(32^{\circ})}{Sin(109^{\circ})} \\ a=853.57\approx854 \\ a=854m \end{gathered}[/tex]Therefore, the distance between the Supermarket and the bank is 854 meters
We will proceed further:
[tex]\begin{gathered} \frac{Sin(A)}{a}=\frac{Sin(B)}{b}=\frac{Sin(C)}{c} \\ \frac{Sin(39^{\circ})}{c}=\frac{Sin(109^{\circ})}{1,523} \\ \text{Cross multiply, we have:} \\ c\times Sin(109^{\circ})=1,523\times Sin(39^{\circ}) \\ c=\frac{1,523\times Sin(39^{\circ})}{Sin(109^{\circ})} \\ c=1,013.68\approx1,014 \\ c=1,014m \end{gathered}[/tex]Therefore, the distance between Ivy’s house and the Supermarket is 1,014 meters