The line segment [S, E], shown below, represents an airport runway - Leaving Cert Mathematics - Question 9 - 2021

To plot the flight path of the aircraft:

1. Start at point S on the diagram.
2. Move 1250 m towards point L, which is approximately 5 units (since 1 unit = 250 m).
3. Draw a line from L to a new point directly above E, maintaining the angle of 14°. Use trigonometric principles to find the vertical distance to ensure the path is accurate.
4. Draw this path on the diagram, making sure that it follows the indicated angle appropriately.

To find the total distance travelled by the aircraft when it is directly above E:

1. The initial distance from S to L is 1250 m.
2. Apply the cosine rule to find the additional distance to E after L:

Let h be the height reached at point L, represented by $h = \frac{1250}{\cos(14^\circ)}$

Calculating this gives

1. Calculate ( \cos(14^\circ) ) and find h:
2. Total distance => h + 1250 m = ( 1250 + h ).
3. Round the final answer to the nearest metre for clarity.

To find the distance from airport B to airport C:

1. Use the sine rule in the triangle formed by points A, B, and C.
2. Represent the lengths and angles according to the sine rule:

Let distance BC = x, then according to the sine rule:

$\frac{x}{\sin(47^\circ)} = \frac{260 km}{\sin(36^\circ)}$

3. Solve for x:

$x = \frac{260 \sin(47^\circ)}{\sin(36^\circ)}$ 4. Compute x and round to the nearest km.

To calculate the total distance travelled:

1. Consider the circular arc the plane flew. The formula for the arc length is:

$C = 2\pi r \left( \frac{\theta}{360} \right)$

Here, r = 10 km (from the problem statement) and ( \theta = 70^\circ ). 2. Calculate C, adding the distance of the circular portion to those previously flown: 3. Total distance = Distance from C to the circle + Arc length + return from the circle to C. Provide the complete answer rounded to two decimal places.