Question

Three city streets form a right triangle. Main Street and State Street are perpendicular. Laura Street and State Street intersect at a 50° angle. The distance along Laura Street to Main Street is 0.8 mile. If Laura Street is closed between Main Street and State Street for a festival, approximately how far (to the nearest tenth) will someone have to travel to get around the festival if they take only Main Street and State Street?

Answer 1

Distance a person has to travel to get around the festival if they take only Main Street and State Street is 1.1 mile

Explanation:

We need an illustration of the scenario in the question:

We are informed Laura street is closed for a festival. To get around the festival by taking Main street and State street, we need to find the distance along Main street and State street as well as the distance along State street and Laura street

To get the distance along Main street and State street, we will apply sine rule

$\begin{gathered} \sin \text{ 50}\degree\text{ = }\frac{opp}{hyp} \\ \sin \text{ 50}\degree\text{ = }\frac{opp}{0.8} \\ \text{opp = 0.8(sin50}\degree) \\ \text{opp = 0.6128} \end{gathered}$

To get the distance along State street and Laura street, we will apply cosine rule

$\begin{gathered} \cos \text{ 50}\degree\text{ = }\frac{\text{adj}}{\text{hyp}} \\ \cos \text{ 50}\degree\text{ = }\frac{adj}{0.8} \\ \text{adj = 0.8(}\cos \text{ 50}\degree) \\ \text{adj = 0.5142} \end{gathered}$

Distance a person has to travel to get around the festival if they take only Main Street and State Street = distance along Main street and State street + distance along State street and Laura street

= 0.6128 + 0.5142

= 1.1270

To the nearest tenth = 1.1 mile

Distance a person has to travel to get around the festival if they take only Main Street and State Street is 1.1 mile