The diagram below shows a cyclic quadrilateral TSMR - NSC Technical Mathematics - Question 6 - 2024 - Paper 2

To find the size of ∠M, we use the property that the sum of angles in a triangle equals 180°.

Thus:

$M = 180° - 67° - 42.5° = 70.5°$

Using the sine rule in triangle SMR:

$\frac{SM}{ ext{sin} R} = \frac{SR}{ ext{sin} R₁}$

From the sine rule:

Rearranging gives:

$SM = SR \times \frac{ ext{sin} R}{ ext{sin} R₁}$

Using previously computed values:

$SM = 22.33 \times \frac{ ext{sin}(42.5°)}{ ext{sin}(70.5°) }$

Calculate:

$SM ≈ 22.33 \times 0.68199 ≈ 16.39 ext{ m}$

To determine the area of ΔSMR, we can use the formula:

$ext{Area} = \frac{1}{2} \times SR \times SM \times \text{sin} M$

Where:

• The area in square metres required depends on the computed lengths and angle.
• Since one bag covers 15178 square metres, number of bags required is:

$\text{Number of bags} = \frac{ ext{Area}}{15178}$