Math problem help, need to understand work process?

Question

A highway is being built between two towns, one of which lies 35.0 km south and 72 km west of the other. What is the shortest length of highway that can be built between the two towns, and at what angle would this highway be directed with respect to due west?

The answers are 80.1 km and 25.9 degrees south of west, but I need to understand the process.

I was setting up the problem as a right triangle with one side 35km and the other side 72 km and using the Pythagorean Theorum, but it doesn't produce the right answer. I don't think I'm setting up the problem correctly.

Answer 1

You get the distance from the pythagorean theorem. I've given 3 web sites that explain it.

The angle is found by trigonometry. The tangent of the angle is 35/72, so you use your calculator to find the "inverse tangent", that is, what angle has a tangent equal to 35/72.

Answer 2

Sorry for my poor English.
A
|
| 35 km
| _________________B
.............72 km

Shortest route between A and B is a straight line:
Using Pythagoras:
AB = SQRT (35^2 + 72^2) = 80.1

For the angle: Use the tangent-formula. An angle of how many degrees corresponds with a tangent of 35/72?

Answer 3

To find the distance you need to use the Pythagorean equation.
distance = square root of ( 35^2 + 72^2)

For the angle you need to use trigonometry.
Tangent of angle = 35 / 72

Hope this helps.

Answer 4

Consider a right triangle with side A of distance 35km, side B of distance 72km, and side C^2 = A^2 + B^2 = 80.1km.

I'm not sure about the angle but I think it could be arcsine(opp/hyp) = q where q is the angle in question.

Answer 5

Start by drawing a diagram. Then use the tangent function to get the angle. Then use the sine or cosine function to get the distance.

Answer 6

use that one theorem...sh*t....whats it called?? oh! pythagorean. and then you use your sine and cosine stuff.