Question 21 – 1.7.13 Arc length and area of a sector (A-level only) - Questions

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 $C$ .

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 $- 6.5$ .

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 $B E$ .

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 $C B E D$ .

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

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

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 $B E$ .

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 $C B E D$ .

1.7.13 Arc length and area of a sector (A-level only)

Question 18

1.7.13 Arc length and area of a sector (A-level only)

Question 18

1.7.13 Arc length and area of a sector (A-level only)

Question 18

1.7.13 Arc length and area of a sector (A-level only) Questions

1.7.13 Arc length and area of a sector (A-level only)

Question 18

1.7.13 Arc length and area of a sector (A-level only) Questions