Question

Find the value of X. Round to the nearest tenth. 7.4in 2.4in x

Answer 1

Answer:

4.4 inches

Step-by-step explanation:

Here, we are interested in calculating the value of x.

Mathematically, a line that comes from the center of the circle and extends to a chord, divides the chord into two equal parts.

This means what we have is a right angled triangle with the radius being the hypotenuse, the half of the length of the chord as the other side of the triangle.

3.7 is half the length of the chord i.e 7.4/2

Thus;

using Pythagoras’ theorem

x^2 = 2.4^2 + 3.7^2

Pythagoras’ posited that the square of the hypotenuse is equal to the sum of the squares of the other two sides of the triangle.

Thus;

x^2 =5.76 + 13.69

x^2 = 19.45

x = √(19.45)

x = 4.41 inches which is 4.4 inches to the nearest tenth

Answer 2

Answer:

Central angle = 31 / 4 radians

=

Length of the arc = (3 1 / 4) (radius) = 45 in

=

=> radius = 45 in * 4 / (31) = 45 * 4 / (3 * 3.14) in

=

radius = 19.1 in

=

Answer: 19.1 in

Step-by-step explanation:

Correct me if I'm wrong