Question

A jewelry company prints a hidden logo watermark. The watermark is a chord that is 0.8 cm from the center of a circular ring that has a r = 3 cm radius. What is the length of the chord to the nearest tenth?

Answer 1

Answer:

length of chord is 6cm

Step-by-step explanation:

Here, we are to calculate the length of the chord.

It should be understood that the chord has a length of 0.8cm from the center of the circle of radius 3cm, thereby forming two right-angled triangles with the radius 3cm being the hypotenuse of each and 0.8cm being the height of each.

Now, the chord is divided into 2 by this height dropping from the center of the circle. To calculate the first half, we use Pythagoras’ theorem with 3cm being hypotenuse and 0.8cm being the other side.

mathematically;

3^2 = 0.8^2 + l^2

9 = 0.64 + l^2

l^2 = 9-0.64

l^2 = 8.36

l = √(8.36)

l = 2.89 approximately

The length of the chord would be 2l = 2 * 2.89 = 5.78 cm which is 6cm to the nearest length