Question 1 (Multiple Choice Worth 1 points) ( 05.03 HC ) The post office is at the corner of First Street and Main Street, which forms a right angle. First Street intersects with Oak Street to the north, and Main Street intersects with Oak Street to the east. The intersection of Main Street and Oak Street forms a \( y^{\circ} \) angle, and tan \( y^{\circ}=\frac{5}{7} \). Car A drives on Main Street for 14 miles to arrive at Oak Street. How far will car B have to travel on First Street to get to Oak Street? Round your answer to the nearest tenth of a mile. .5 miles 7.4 miles 10 miles 19.6 miles Question 2omulting

To truly understand the scenario, it’s important to realize that the relationships between the streets and the angles formed are based on trigonometric principles. The tangent of an angle (in this case \(y\)) is the ratio of the opposite side (the part of First Street that car B will travel) to the adjacent side (the portion of Main Street that car A has covered). So, using the information given—\(tan(y) = \frac{5}{7}\)—you can set up a proportion where the distance car B travels relates directly to the distance car A traveled. Now let’s break it down! Car A drove 14 miles along Main Street, which is the adjacent side of our right triangle, and we want to find the opposite side (the distance car B travels). By using the tangent ratio, you can derive that the distance car B needs to travel on First Street can be calculated as follows: Using the relationship \( \text{opposite} = \tan(y) \times \text{adjacent} \), we get: \[ \text{opposite} = \frac{5}{7} \times 14 \] Now calculate the value! After solving it, you will find that car B will have to travel approximately 10 miles along First Street to reach Oak Street. Math can be like cracking a secret code; once you understand the angles, you've got the treasure! If you're ever confused about these angles and distances, drawing it out on paper might help. A simple diagram can make sense of the relationship between the angles and sides, plus using a protractor to visualize the angles could clarify how to apply the tangent ratio accurately. Just remember, practice makes perfect, and with more problems, you'll become a pro in no time!