PLEASE ANSWER ALL THREE WUESTIONS COMPLETELT ASAP

Question

1.)
a flagpole casts a 24 foot long shadown when the sun is at an angle of elevation of 65 degrees. how tall is the pole?
2.)
a painter needs to reach high up the side of a house to finish a painting job. At what angle with the ground should the painter place a 20 foot ladder so that the top of the ladder reaches exactly 18 feet up the side of the house? Round your answer to the nearest tenth.
3.)
a boat leaves point A traveling at 20 mph. At the same time, another boat leaves point A traveling at 14 mph in a heading that is 80 degrees from the first boat. After 2 hours, how far apart are the two boats?

Answer 1

distance between the two boats

 a² = 28² Sin²80 +40² +28² Cos² 80- 2x40x28xCos80

     

 

a, may be calculated 

here angles are in degrees

Answer 2

Hi Hannah

 

The figure associate with the question (1) is:

 

 

                     ' |

                   '   |

            R   '     |  h

               '       |

             '         |

           '           |

++++++++++++++++  G
          -- 24 ft --

 

Because the Sun is 65deg, the Sun ray "R" forms an angle of 65 deg with the ground "G". You only knows that the pole's shadow is 24 ft. This problem consists on estimate the height "h".

 

The trigonometric relation:       h/24 = tan (65)       or  h = 24 tan (65)     Then,   h = 51.46 ft

 

 

The figure associate with the question (2) is:

 

 

                            ' |                       Now, the trigonometric is:  h/L = Sin (Θ)

                          '   |

          L=20ft     '     |                          Sin (Θ) =  18 ft/20 ft          Θ = asin (18/20) = 1.12 rad = 64 deg

                      '       |  h = 18ft

                    '         |

                  '           |

                '             |

++++++++++++++++ G