Really Hard Trig Question

Question

A tree grows vertically on a slope which has an incline of 25 degrees. When the sun is at an elevation of 77 degrees, the tree casts a shadow of 50 feet directly down the slope. What is the height of the tree?

Answer 1

 

          A

          /|

         / |

        /  |

       /   |

      /    | h

     /     |

    /      |

   /       |

  /    a    B

 H    

 

[sorry, can't draw in the application.]

 

1. Slope from H to B is 25

    Slope from H to A is 77

    therefore the angle AHB is 77-25 = 52 degrees

 

2. the angle HBA is 25+90 = 115 degrees [draw a line parallel to the ground through B. Alternating interior angle will be 25 plus the right angle going vertical.]

 

3. Therefore angle HAB (at the top) is 180 - 52 - 115 = 13 degrees

 

Using Law of Sines

 

sin(HAB)      sin(AHB)

----------  = ------------

length a       length h

 

or, sin(13)      sin(52)

     --------  =  --------

         50             h

 

solve for h = approx 175 feet