word problem need help asap

Question

A boat travels 8 miles north from point A to point B. Then it moves in the direction S 40º W and reaches point C. Finally, it turns S 40º E  and returns to point A. Whats the total distance covered by the boat is how many miles?

Answer 1

 

                                     B

                                     •

                                     |

                              40º |

                                     |

                                     | 8 miles

              C  •  40°         |

                                     |

                                     |

                                     •

                                     A

 

This scenario represents a triangle.

 

Let a = side of triangle opposite angle A

Let b = side of triangle opposite angle B

 

Angle A measures 100° ... the sum of the internal angles of all triangles is 180°.

We need to determine the unknown sides of the triangle to find the perimeter.

The perimeter of the triangle represents the total distance covered.

 

We can use the law of sines.

 

    a/(sine A) = c/(sine C)

 

    a/(sine 100°) = 8/(sine 40°)

    a = ((sine 100°) • 8)/(sine 40°)

    a = 12.26

 

    Since angle C = angle B, side c = side b

    If the anfles of a triangle are congruent, the sides opposite those angles are congruent.

 

    b = 8

 

The total distance traveled is equal to the perimeter of the triangle.

 

    12.26 + 8 + 8 = 28.26

 

Total distance is 28.26 miles.