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Trigonometry - Angles of elevation & depression.
Test Yourself 1 - Solutions.


 

Angles of elevation.  
   
   
   
  5.
Angle of depression. 6.
   
   
   
  10.
Both types. 11.

(i)

(ii)

 

12. (i) Tan EFD = 254/37 = 81° 43'

Angle of depression of D from F = 90° - 81°43' = 8° 7'.

(ii) 165 = AE + EF = AF + 37

AF = 128 cm

DC also equals 128 cm because ACDE is a rectangle.

(iii) GB = 196 = 9 + 128 + CB

CB = 59 cm.

(iv) Tan CAB = 59/254

CAB = 13° 5' which is the angle of depresion of B from A.

(v) FD is not parallel to AB - the angles differ by 4° 58'.

(vi) The area ABDE is made up of a rectangle and a triangle.

Arearectangle = 128 × 254 = 32,512 cm2.

Arealower tri = 1/2 × 254 × 59 = 7493 cm2

Total = 40,005 cm2 = 4 0 m2 (because 1 m2 = 100 × 100 cm2 = 10,000 cm2.