Lesson 1, Topic 2
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Scale Drawing

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Example 3

The diagram below shows a right-angled triangle

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

b. Using Pythagoras theorem

x2 = 82 + 72

x2 = 64 + 49

x = $$\scriptsize \sqrt{113} \\ = \scriptsize 10.6m$$

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.

Responses error: