10.1 A double-headed rotating sprinkler (as shown in the picture below) is used to irrigate a circular vegetable garden - NSC Technical Mathematics - Question 10 - 2021 - Paper 2

To calculate the length of chord ED, we can apply the Pythagorean theorem:

1. Identify the radius of the smaller circle (OB): 4 m

2. Determine the height of segment (h):

   $h = 2.95 ext{ m}$

3. Using the formula for the half chord, we start with:

   $x^2 + h^2 = r^2$

   where:

   • r is the radius of the smaller circle (4 m)
   • x is half the length of the chord ED.

   Substitute:

   $x^2 + (2.95)^2 = (4)^2$

   $x^2 + 8.7025 = 16$

   $x^2 = 16 - 8.7025$

   $x^2 = 7.2975$

   $x = ext{sqrt}(7.2975) ext{ m} \ ext{ and thus, } x ext{ approximately } 2.70 ext{ m}$

4. The length of chord ED is:

   $ED = 2x = 2(2.70) = 5.40 ext{ m}$

Thus, the length of chord ED is 5.40 m.