Two forces P and Q act on a particle at a point O - Edexcel - A-Level Maths Mechanics - Question 5 - 2008 - Paper 1

To find the value of X, we apply the cosine rule. The relationship can be expressed as:

$X^2 = R^2 + 15^2 - 2 \cdot R \cdot 15 \cos \theta$

where $\theta = 100^{\circ}$ (since the angle is supplementary to 50°). Now substituting $R \approx 9.79$ N, we can calculate:

$X^2 = 9.79^2 + 15^2 - 2 \cdot 9.79 \cdot 15 \cos 100^{\circ}$

After computing each term, substituting the cosine value using a calculator gives:

• $\cos 100^{\circ} \approx -0.173$.

Thus, we find:

$X^2 \approx 9.79^2 + 15^2 + 2 \cdot 9.79 \cdot 15 \cdot 0.173$

Calculating this step-by-step leads us to:

$X \approx 19.3 \text{ N}$