The diagram shows a running track $ABCD$. $D$ is a point on the straight line $EC$. It is give

Question

The diagram shows a running track $ABCD$. $D$ is a point on the straight line $EC$. It is given that $AB = 280\text{ m}$, $AD = 150\text{ m}$, $\text{angle}\hspace{0.5em} BCD = \text{angle}\hspace{0.5em} DAB = 90^\circ$ and $\text{angle}\hspace{0.5em} ADE = \theta$, where $0^\circ < \theta < 90^\circ$. Show that $L\text{ m}$, the length of the running track, is given by $L = p + 130\cos\theta + 430\sin\theta$, where $p$ is a constant.[3] Express $L$ in the form $p + R\cos(\theta - \alpha)$, where $R > 0$ and $\alpha$ is an acute angle.[3] Xin Ting ran five complete laps around the track. She claims that she ran a total of $5\text{ km}$. Explain why she might be wrong.[2] Given that the running track is $700\text{ m}$ long, find the value of $\theta$.[3]

Accepted Answer

(b) $430 + 449\cos{( \theta - 73.2^{\circ})} $ (d) $\theta = 20.1^{\circ} $

2024 CGSS P1 Q10

2024 CGSS P1 Q10