Due Date: Friday February 12, midnight

Submit your individual file (hw3.py) with the Canvas link.

Reminder that "Individual" means that you should not talk to another student in the class about it. You ARE encouraged to talk to any TA or your lecturer.

Educational goals of this lab - verify that every student can

• Use the import statement
• write function calls
• use input and output statements
• write an arithmetic expression

INSTRUCTIONS:

• Problem Description:

  Scientists studying a forest ecosystem over a long period of time may record measurements of trees for a number of variables, including each tree's diameter at breast height, height of the lowest living branch, canopy cover, etc. One aspect of a tree's growth that can be hard to measure is tree height. The easiest way to find the height is using a trigonometric function. If you know the distance you are from the foot of the tree, the angle that the top of the tree makes from the ground (your eye) (angle of elevation), and your height from the ground to your eye level, you can calculate the height of the tree.

  
• (12 points) Individual Problem #1: Test Cases

  Put the answers that go in the blanks below into a triple-quoted comment at the bottom of the program file. It should be the expected output (height) from the above program, given the inputs in the case. Use a calculator as needed. Note that you will have to put the calculator in "degrees" mode. For each test case, you get two points for getting the correct answer by hand, and 1 point for your program running it correctly.

  Description	Inputs Angle of Elevation (deg), distance to tree (ft) height of observer to eyes (ft)	Expected Output Height (ft)
  Normal case, integers	45, 50, 5	____A.____
  Normal case, floats	75.0, 92.5, 4.9	____B.____
  Point of view at base of tree	89.5, 0, 5.1	____C.____
  Negative angle	-10.0, 100, 5.2	____D.___

• (10 points) Individual Problem #2: Design
  • As usual, write a prolog with your info, and the 3 P's (purpose, pre-conditions, post-conditions).
  • Use this design and complete it.

    # Purpose: 
    # Pre-cond: 
    # Post-cond: 
    
      # use math library for radians function needed to convert input angle to radians
      # and tan function used to calculate height
    
      #print title and blank line
    
      #get 3 input values, angle of elevation, distance to base and height of observer
    
      # COMPLETE the steps needed here
    
      # report resulting height, using 2 decimals
    

• (38 points) Individual Problem #3:
  • Write a program which will calculate the height of the tree using the tangent trigonometric function. Do not worry if trig is not your best subject. The formula is given above, next to the picture. The main purpose of this program is to learn how to import functions from a library and call functions.
  • The input of the angles must in degrees.
  • Note that the argument of the tan function must be in radians. You must use a math library function called radians. It has one argument (in degrees) and returns (float) the equivalent in radians.
  • You must use the math library for the radians and tan functions.
  • The output of the result should be formatted to show 2 decimal places.

    Test run 1:

    Finding the height of a tree
    
    Angle of elevation to top of tree (deg): 49
    How far to the base of the tree (ft)? 500
    Your height up to your eyes (ft)? 5.1
    The height of the tree is 580.28 feet
    

    Test run 2:

    Finding the height of a tree
    
    Angle of elevation to top of tree (deg): 35.2
    How far to the base of the tree (ft)? 30
    Your height up to your eyes (ft)? 4.8
    The height of the tree is 25.96 feet
    
    

• Turn in your source file (hw3.py file) with the Canvas link.
• Deadline to turn it in is Friday, February 12, midnight. If you turn it in after that but before 9 am the next day, you will lose half the points. If you turn it in any later than that, you lose all the points.