5.2 Arc Length

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A coastal surveillance system uses two intersecting paths for its detection beams, $p_1$ and $p_2$ . The primary path $p_1$ follows the line with equation $4 y + 3 x = 24$ . The path $p_1$ intersects the $y$ -axis at the point $C$ .

State the $y$ -coordinate of $C$ .

[1]

A tracking station is located at the point $D (6, 1.5)$ , which lies on $p_1$ . A secondary beam $p_2$ originates from $D$ and is directed perpendicular to $p_1$ . The beam $p_2$ intersects the $y$ -axis at the point $E$ .

Show that the $y$ -coordinate of $E$ is $- 6.5$ .

[3]

A circular scanning sector $B C E$ is defined with centre $C$ and radius $C E$ . Given that the central angle $B C E$ is $0.8$ radians,

find the length of the arc $B E$ .

[2]

The combined detection zone $C B E D$ is formed by the sector $B C E$ and the triangular region $C D E$ .

Calculate the exact area of the combined detection zone $C B E D$ .

[4]

5.2 Arc Length Questions

Practise Edexcel A Level Maths 5.2 Arc Length with exam-style questions for A Level Maths. 2 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.