Die lengte van SR SR = TS² + TR² - 2 * TS * TR * cos(67°) SR = (22)² + (18)² - 2(22)(18)cos(67°) SR = 498.5409462 SR = 22,33 m Die grootte van M M̂ = 180° - 67° - 113° - NSC Technical Mathematics - Question 6 - 2024 - Paper 2

We find the angle M̂ by applying the formula:

$M̂ = 180° - 67° - 113°$

Thus:

$M̂ = 113°$

Using the sine rule, we have:

$\frac{SM}{\text{sin}(R̂)} = \frac{SR}{\text{sin}(M̂)}$

This can be rearranged as:

$SM = \frac{SR \cdot \text{sin}(R̂)}{\text{sin}(M̂)}$

Substituting values:

$SM = \frac{22.33 \cdot \text{sin}(42.5°)}{\text{sin}(113°)}$

Continuing from the previous calculations, we need:

$SM = \frac{22.33 \cdot 0.6745}{0.8387} \text{ (values for sin(42.5°) and sin(113°))}$

Carrying out this computation gives us:

$SM \approx 16.39 m$

To calculate the area of triangle ΔSMR, we can use:

$\text{Area} = \frac{1}{2} \times SR \times SM \times \text{sin}(R̂)$

Substituting the known values:

$\text{Area} = \frac{1}{2} \times 22.33 \times 16.39 \times \text{sin}(42.5°)$

Calculating this gives us:

$\text{Area} \approx 15.178 \text{ square meters}$

Now, to find the number of bags required:

We know that each bag covers 15.178 m². Thus:

$\text{Bags required} = \frac{15.178}{7.5} \approx 2 bags$