High School Level Physics Homework

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SUMMARY

The shortest length of highway between two towns located 35.0 km south and 72.0 km west of each other can be calculated using the Pythagorean theorem. The distance is determined by the formula A^2 + B^2 = C^2, where A and B are the legs of the right triangle formed by the towns. The calculated distance is approximately 83.0 km, and the angle with respect to due west can be found using trigonometric functions, specifically tangent, yielding an angle of approximately 26.57 degrees.

PREREQUISITES
  • Understanding of the Pythagorean theorem
  • Basic knowledge of trigonometric functions (sine, cosine, tangent)
  • Ability to visualize and sketch right triangles
  • Familiarity with coordinate systems
NEXT STEPS
  • Study the application of the Pythagorean theorem in real-world scenarios
  • Learn how to calculate angles using trigonometric ratios
  • Explore graphing techniques for visualizing geometric problems
  • Investigate the use of trigonometry in construction and engineering
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High school students tackling physics homework, educators teaching geometry and trigonometry, and anyone interested in applying mathematical concepts to real-world problems.

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Homework Statement


A highway is to be built between two towns, one of which lies 35.0km south and 72.0km 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.

Homework Equations


A^2 + B^2 = C^2 ... this might be used, I am unsure.

The Attempt at a Solution


I know that this involves the trig functions sin, cosine, and tangent. This is the first homework problem of the section and I am having trouble visualizing it. Please help. Thanks!
 
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Try drawing a quick sketch on graph paper roughly to scale showing a point for town A at the origin and another point for town B located as given at x ='-72 and y = -35. A line drawn from A to B is the shortest distance between the 2 and will be the hypotenuse of the right triangle with the leg dimensions as given. Looks like Pythagoras will give you the distance and a little trig (you know SOH-CAH-TOA?) will give the angle.
 

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