A highway is to be built between two towns, one of which lies 33.5 km south...

A highway is to be built between two towns, one of which lies 33.5 km south and 70.8 km west of the other. (a) What is the shortest length of highway that can be built between the two towns, and (b) at what angle would this highway be directed, as a positive angle with respect to due west?

Solutions

Expert Solution

Call the starting town Town A, and label it with a point called A. Now, draw a line straight, south of this point. The length of the line is 33.5. Draw a line from the end of the line you just drew. It should be going west, and its length is 70.8. The end of the line you just drew is the second town, Town B. What we have is a right triangle. The shortest distance is always the straight line distance. We have the other 2 sides of the right triangle. Using thePythagorean theorem we get:

a^2 + b^2 = c^2
33.5^2 + 70.8^2 = c^2
c = 78.3255km

78.3255km is shortest length highway between the towns.

What angle with respect to west. This means the angle between the line going west and the hypotenuse. I'll call that angle theta.

Therefore, tan theta = opposite/adjacent = 33.5/70.8
theta = arctan(33.5/70.8) Note: arctan means inverse tan (tan^-1 on your calculator)
theta = 25.32degrees south of west

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

There are two towns. In one of them, about 1/6 of them are infected by a...

There are two towns. In one of them, about 1/6 of them are infected by a virus, while the other is free of disease. You have no idea which town is infected and which is not. But you do have a test to detect this virus in patients. It is a time consuming test, so you can only do the test twice. If a person has the virus, then the test shows positive for the virus (with probability 1). If...

Motion in two dimensions. A plane is flying due south at 560 km/h. A wind blows...

Motion in two dimensions. A plane is flying due south at 560 km/h. A wind blows the plane from east to west at 95 km/hr (yikes!) Find the plane’s velocity with respect to the ground. A projectile is shot from the edge of a cliff 258 m above ground level with an initial speed of 95.0 m/s at an angle of 22 degrees with the vertical. Find the time taken by the projectile to hit the ground. Now find the...

Highway engineers estimate that the main highway between two cities has a 1% probability of being...

Highway engineers estimate that the main highway between two cities has a 1% probability of being blocked in good weather, and a 5% probability of being blocked in snowy weather. The detour route, on the other hand, is a smaller road which has a 2% probability of being blocked in good weather and a 15% probability of being blocked when it snows. On a certain day, forecasters predict a 60% chance of snow. a. Are the events that it snows...

Kenya and South Africa are trading partners, and there are capital flows between the two countries....

Kenya and South Africa are trading partners, and there are capital flows between the two countries. The currency in Kenya is the Kenyan shilling (Ksh.) and the currency in South Africa is the South African Rand (R). Assume that the equilibrium exchange rate is 0.14R per Kenya shilling. Now suppose that the opportunity cost of consumption falls in South Africa. Referring to the Kenyan foreign exchange market, explain how the equilibrium exchange rate might change. You are not required to draw...

A train runs between San Diego, and Kansas City, which is 4 km apart and maintains...

A train runs between San Diego, and Kansas City, which is 4 km apart and maintains voltages of 450 volts and 400 volts respectively. The resistance of go and return is 0.05 ohm per km. The train draws a constant current of 500 A while in motion. What are the currents supplied by the two stations if the train is at the distance of minimum potential?

A horizontally projected beam of protons travels at 55 km/s into the space between two horizontal,...

A horizontally projected beam of protons travels at 55 km/s into the space between two horizontal, parallel plates. The plates are separated by 7.4 cm, and they are 12 cm long. There is a uniform electric field between the plates of unknown strength. The beam enters the region exactly midway (vertically) between the plates and exits the region 7.2 microns closer to the lower plate. If it were a beam of electrons instead, everything else being the same, at what...

As SR361 enters Middletown from the NW, it must curve to the south between two historic...

As SR361 enters Middletown from the NW, it must curve to the south between two historic buildings. At this point, SR361 consists of two 11-foot lane. The building to the right of traffic, is only 10 feet from the edge of the 5-foot wide shoulder. Local policy is that the superelevation rates not exceed 0.06 inches per inch. Will the minimum SSD be available from vehicles moving at 60 mph through this curve?

The highway department must select one of two repair options for a 10-mile of a four-lane...

The highway department must select one of two repair options for a 10-mile of a four-lane highway. The analysis period is 8 years and interest rate (MAAR) is 8% Option 1 Option 2 Initail Cost 5,300,000 3,000,000 Annual cost 300,000 400,000 Lifetime 8 years 4 years a) Using Present worth analysis, find the best repair option. b) Using Annual worth analysis, find the repair option. c) Using incremental rate of return analysis, find the best repair option. Use the shortcut...

One hundred students were placed into two groups. The two groups were the South Beach diet...

One hundred students were placed into two groups. The two groups were the South Beach diet and Keto diet. Below are the data for pounds lost after 1 month of dieting. Assume the data are normal and that the sample size is 100 (but, use the values you have). Tell me if there is a difference between the two diets. Show all of your work. SB Keto 2.5 3.5 3.2 3.7 3.0 4.0 5 4.1 2.3 4.0 2.7 2.5 1.0...

Which of the following is always true regarding the relationship between the one- and two-tailed significance...

Which of the following is always true regarding the relationship between the one- and two-tailed significance tests? Select all that are true. If the one-tailed test is significant, then the two-tailed test at the same α will also be significant. If the two-tailed test is significant, then the one-tailed test at the same α will also be significant (in the appropriate direction). If the two-tailed test is significant, then the one-tailed test at the same α may...

Subjects