Question
MAPS Sata is going to Texas to visit a friend. As she looked at a map to see where she might want to go she noticed that Austin Dallas, and Abilene form a triangle. She wanted to determine how the distances between the cities were related, so she used a protractor to measure two angles. a. Based on the information in the figure,which of the two cities are nearest to each other? square b. Based on the information in the figure.which of the two cities are farthest apart from each other? square c. If you were going to use the information from Sata's sketch to plan a road trip between th these cities what is an assumption that you would have to make? square disappointed
Solution
4.3
(209 Votes)
Sebastian
Master · Tutor for 5 years
Answer
a. To determine which of the two cities are nearest to each other, we need to look at the angles given in the triangle. The larger the angle opposite a side, the longer the side will be. Since we have two angles:- The angle between Dallas and Abilene is 64°.- The angle between Abilene and Austin is 59°.The third angle in the triangle can be found by knowing that the sum of angles in a triangle is always 180°. So, the angle between Dallas and Austin would be:180° - 64° - 59° = 57°.Now, since the angle between Dallas and Abilene is the largest (64°), the side opposite this angle (the side between Austin and Abilene) is the shortest. Therefore, the nearest cities to each other are:Answer: Dallas and Abilene.b. The cities that are farthest apart from each other will be opposite the largest angle. Since we have determined that the angle between Dallas and Abilene is the largest, the cities farthest apart are:Answer: Abilene and Austin.c. If you were going to use the information from Sata's sketch to plan a road trip between these cities, an assumption that you would have to make is that the roads between the cities are straight lines, which would correspond to the sides of the triangle. In reality, roads may not be straight due to terrain, infrastructure, or other factors, and the actual travel distance could be longer than what is suggested by the straight lines on the map.Answer: The assumption is that the roads between the cities are straight lines.