Measuring Angle of Elevation and Depression

Theodolite: Used by surveyors

Clinometer: Made up of a protractor, a tube, and a plumbline attached to the centre of the protractor to indicate the angle. 

Example 2.3.1: 

From a point A on a level ground 27.5 cm away from the foot of a tower, the angle of elevation of the top of the tower is observed to be 44°. 

(a) Find by scale drawing, the height of the tower. 
(b) How far is point A from the height of the tower? 

Solution

 Step 1: Start by drawing a rough sketch 

Step 2:   Choose a suitable scale. In this case, 1 cm represents 5 cm. 

|AC| = 27.5 cm, 

Scale = \( \frac{1 \: cm}{5\: cm} \)

Scale = \( \frac{any \: length \: of \: scale \: drawing }{\: length \: of \: actual \: object} \)

∴ \(\frac{1}{5} = \frac{length \: of \: scale \: drawing }{27.5} \)

cross multiply

length of scale drawing = \( \frac{27.5}{5} \\ \scriptsize = 5.5 \: cm\)

Step 3:  Draw a horizontal line of length 5.5 cm and draw the triangle using a protractor, using a 44° angle.

Draw a horizontal line of length 5.5 cm

Mark a 44° angle using a protractor