Question

The small side of the rectangle is 20 centimeters. The sharp angle between the diagonals is 60 degrees. Find the radius of the circle described around the rectangle.

a) 10 √3
b) 20
c) 20 √3
d) 30

Answer 1

To find the radius of the circle described around a rectangle, we can use the formula: radius = (diagonal length) / 2. The diagonal length of the rectangle can be found using the small side length and the angle between the diagonals. Finally, the radius of the circle is calculated using the formula, giving the correct option as a) 10√3.

Step-by-step explanation:

To find the radius of the circle described around a rectangle, we can use the formula:

radius = (diagonal length) / 2

First, let's find the length of the diagonal of the rectangle. The small side of the rectangle is given as 20 centimeters, and the angle between the diagonals is 60 degrees. Using the trigonometric relationship, we can find the length of the diagonal:

diagonal length = (small side length) / sin(angle)

diagonal length = 20 / sin(60)

diagonal length = 20 / (√3/2) = 40/√3

Finally, we can find the radius of the circle described around the rectangle:

radius = (diagonal length) / 2 = (40/√3) / 2 = 20/√3 = 20√3/3

Therefore, the correct option for the radius of the circle described around the rectangle is a) 10√3.