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JSS2: MATHEMATICS - 3RD TERM

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Example 3 

The diagram below shows a right-angled triangle 

scale drawing

a. Using a scale of 1cm to 5m, draw the triangle 

b. Find the actual length of the hypotenuse BC. 

c. Measure the two remaining angles 

Solution 

Scale = 1cm to 5cm = \( \frac{1cm}{ 5cm} \\ = \frac{1}{5} \)

AB  =  40m 

On scale drawing AB = \(\scriptsize 40 \; \times \; \normalsize \frac {1}{5} \\ = \scriptsize 8m \)

AB  =  35m 

On scale drawing AC = \(\scriptsize 35 \; \times \; \normalsize \frac {1}{5} \\ = \scriptsize 7m \)

 Draw a triangle with AB = 8m and AC = 7m 

Screen Shot 2021 01 06 at 10.33.38 AM

b. Using Pythagoras theorem

Hyp2 = Opp2 + Adj2

x2 = 82 + 72

x2 = 64 + 49

x = \( \scriptsize \sqrt{113} \\ = \scriptsize 10.6m\)

Screen Shot 2021 02 25 at 12.36.43 PM

By measurement BC = 10.6m 

(c) Using a protractor to measure angles B and C respectively

:- \( \scriptsize \tilde{ABC} = 49^0 \)

:- \( \scriptsize \tilde{ACB} = 41^0 \)

Or

Using SOHCAHTOA to confirm the angles

tanB = \( \frac {opp}{adj} \\ = \frac {7}{8} \\ \scriptsize B = tan^{-1} \left [ \normalsize \frac{7}{8} \right] \\ \scriptsize = 49^0 \)

Also,

tanC = \( \frac {opp}{adj} \\ = \frac {8}{7} \\ \scriptsize C = tan^{-1} \left [ \normalsize \frac{8}{7} \right] \\ \scriptsize = 41^0 \)

Evaluation 

  1. An equilateral triangle has sides 150mm. Using a scale of 1cm to 5cm, draw the triangle 
  2. Use a scale of 1cm represent 40m to draw a scalene triangle of sides 360m, 120m, and 240m respectively.
evaluation scale drawing

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