Scale Drawing

Example 1.2.1: 

The diagram below shows a right-angled triangle 

1. Using a ruler and protractor only and a scale of 1 cm to 5 cm
a. Draw the triangle.
b. Find the actual length of the hypotenuse \( \scriptsize BC \). 
c. Measure the two remaining angles.

2. Using calculations and the scaled triangle;
a. Find the actual length of the hypotenuse \( \scriptsize BC \). 
b. Calculate the remaining two angles. 

Solution 

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

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

\( \scriptsize AB = 40 \: cm \)

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

\( \scriptsize AC = 40 \: cm \)

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

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

Step 1: Draw AC (AC = 7 cm )

Step 2: Draw AB (AB = 8 cm )

Step 3: Complete the Triangle by drawing line \( \scriptsize BC \)

1. b. Find the actual length of the hypotenuse BC. 

Step 4: Measure \( \scriptsize \bar{BC} \\ \scriptsize ⇒ BC = 10.6 \: cm\)

1. c. Measure the two remaining angles 

Step 5: Using a protractor, Measure ∠ACB