Answer Page!!
 
 
1) 
 
Use pythagorean relationship to find c
             ________
    c = \/ 252 + 452  = 51.5

To find / A, use tan A = 25/45.   / A =29.1o
Thus, / B = 90 - 29.1 = 60.9o
 

 
2) 
To find side x, use sin 22 = x/20
The distance from the building to the bottom of ladder is 7.49 feet.
 
b) 
Original height to top can be found by using pythagorean's theorem:
      _________
= \/ 202 - 7.492  = 18.5
You can use pythagorean's theorem to find the new height"
      __________
= \/ 202 - 10.492  = 17.0
Now, subtract to get 1.5 feet.
 
 
3)  To find the area k = .5(281)(358)(sin 43.3) = 34496 square units.
 
 
4) 
To find / C, 180 - (61 + 42) = 77o
 
To find a, use:  a/ Sin 61 = 15/Sin 77
       a = 13.5
To find b, use: b/Sin42 = 15/Sin 77
       b = 10.3
 
 
5)  a)  Since c is bigger than a, we get 1 triangle.
     b)  Since a is bigger than b, we get 1 triangle.
     c)  The shortest distance is 10 sin 30 = 5.  Since the opposite side is smaller than the shortest distance, we cannot form a triangle!
 
6) 
 
 
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9) 
Area of K1 = .5(200)(150)sin 115 = 13595 sq meters.

To find the area of K2, we need to find the length of the purple line above.
Use law of cosines to find  = 2002 + 1502 - 2(200)(150)cos 115 and take the square root.  This is about 296 meters.  Now find the angle between the purple line and 200 line by using the law of sines.  296/sin 115 = 150/sin x.  The angle measures:  27.3.  Thus, the angle at the top is 180 - ( 27.3 + 45) = 107.7o  
The area of K2 = .5(400)(296)sin107.7 = 56398 sq meters.

Add the two areas and round to 3 significant digits
56398 + 13595 = 69993
rounded to 70000 sq meters.
 

 
 Hope you did well!  Get ready for the last section in trig!!