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


 

Angles of elevation.  
   
   
   
  5.
Angle of depression. 6.
   
   
   
  10.
Both types. 11. The diagram below shows a satellite dish S sitting on a foundation TB. The top of the dish is above the right side of the foundation.

The distance from point P to the foundation is 15 m. The distance from P to the top of the dish is 25 m.

(i) Calculate the angle of elevation from P to S (to the nearest degree).

(ii) The angle of depression from T to P is 28°. Find the height of the foundation TB.
(to the nearest metre).

Answer.(i) Angle of elevation is 53°.
(ii) Height TB = 8 m.
  Near my house is a fence between two brick pillars. It is behind a lovely bush and has a small fish pond in front.

The main points and the measurements are marked on the picture below.

The tops of the pillars are marked F and G. The bottom of the pillars are at A and B. FA and GD are perpendicular.

The top of the fence is ED and the bottom of the fence is AB. ED is parallel to AC and both are horizontal.

AF = 165 cm with the top part EF = 37 cm.
Similarly BG = 196 cm with the top part DG = 9 cm.

(i) Find the angle EFD and hence find the angle of depression of D from F.

(ii) Show that AE = CD = 128 cm.

(iii) Show that CB = 59 cm.

(iv) Find the angle of depression of A to B.

(v) Is FD parallel to AB?

(vi) Find the area of the painted timber ABDE (to the nearest m2).

Answer.(i) EFD = 81°43'
∴ Angle of depress = 8°7'.
(iv) Angle of depression = 13° 5'.
(v) No - different angles of depression.
(vi) Area = 4 m2