G. Tawfik          
MATHEMATICS 436

Extra-Review 9B   Trigonometry

                          See: Notes on Trigonometry 





1.    Kim is standing on the balcony of a building, 35 m above
       street level. She is watching an accident at an angle of
      depression of 40o.

      How far is the accident from the base of her building?











2.    As a plane ascends, its path makes a 60o angle with the
       runway. How high does the plane rise when it has travelled
      400 m through the air?





3.    Two surveyors stand at points A and B that are 85 m apart
       along a straight river bank. Point C lies on the opposite bank
       directly across the river from B.
       The surveyor at A finds that  < BAC = 60o.
       Find the width of the river at B.










4.    A road rises 4 m per 100 m along the horizontal. What angle  
      does the road make with the horizontal?






5.    From  point G on level ground, the angle of elevation of the
       top of the CN tower is measured to be 31o. From point K,
      130 m closer to the tower, the angle of elevation is 35o.
      What is the height of the CN tower according to these    
      measurements?






6.    From points R and E, 2 km apart, Robert and Erin observe
       a kite K in the sky. Robert’s angle of elevation is 62o and Erin’s
       angle of elevation is 32o. How high is kite K?






7.    Determine the value of x in each of the given figures:
a.
 

b.

c.
 

d.

 

8.    From opposite ends of the Simplon tunnel between Italy
       and Switzerland, the angles of elevation to the peak P are
      14o and 28o. If the peak is 2130 m above the tunnel,
      determine the length of the tunnel.







9.    In each of the following triangles, determine the missing dimension:
a.


 b.
c.

 d.