Trig story problems

Question

A hiker travel 7.5 hrs at 3.5 miles per hour at a heading of S 58° from a ranger station.

 

A. How far is hiker from ranger station?

 

B. How far east is the hiker from the ranger station

Answer 1

7.5 hours at 3.5 mph

7.5(3.5) = 26.25 miles

 

Draw a triangle.

 

From point A.. Ranger station

draw a line to south east at 58^o

 

That line is 26.25 miles for length

 

Draw a 2nd line horizontally right from the ranger station to east

stopping directly above the end of the southeast line.  Point B.

 

Connect point B vertically to the far end of the hypotenuse.. Point C

 

         a

  A ______B

     \58     |

      \        |

        \      |

 26.25\     | b

           \   |

             \ |

              \|

               C

 

We now have a right triangle

The hypotenuse is 26.25 miles long

The horizontal east line is length a

The vertical south line is length b

 

We want the east distance or, the length of side a

 

Using the cosine function we have:

cos(A) = adjacent/hypotenuse

 

Cos(58) = a/26.25

 

a = 26.25[Cos(58)]

 

a = 13.91 miles

 

If you need the south distance use the

Pythagorean theorem  a²+b²=c²

13.91² + b² = 26.25²

 

b = √(26.25² - 13.91²) = 22.26 miles