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Trigonometry - Radial surveys.
Test Yourself 1.


 

   
   
  3. The results of a radial survey of a block of land are shown below.

(i) Show that the size of ∠DOA = 105°.

(ii) Determine the sizes of the other three angles at the centre.

(iii) Find the length of the distance
from D to A.

(iv) Find the area of triangle COB.

 
  4. A radial survey of a paddock is drawn below.
The length measurements are in metres.

(i) Show that ∠AOD = 132°.

(ii) Calculate the length of AD (to the nearest metre).

(iii) Show that the ratio of the areas of triangles AOB and BOC is approximately 3:2.

 
 

5. A basic radial survey of a property in South Australia is determined from a high altitude image. It is summarised in the following diagram.

(i) Find the size of all the angles at the centre.

(ii) Find the length of the boundary XY.

(iii) Find the length of the total boundary XYZ.

(iv) Find the area of the section YOZ.

(v) Find the total area of the property.

 
  Manly 2019 Q30