Question

A roulette wheel of radius 120 cm has two numbers on its rim. the distance along the rim between the numbers is 4 cm. find the angle subtended at the center of the wheel by the numbers. give your answer in degrees. express your answer correct to two decimal places.

Answer 1

The angle subtended at the center of a roulette wheel with a 120 cm radius by two points on its rim 4 cm apart is 1.91 degrees.

Step-by-step explanation:

To find the angle subtended at the center of a roulette wheel by two numbers on its rim, we need to use the relationship between the arc length and the radius of the circle. In this case, the radius given is 120 cm and the distance along the rim between the two numbers is 4 cm. The formula to calculate the subtended angle (in radians) is ϴ = s / r, where 's' is the arc length and 'r' is the radius of the circle.

First, convert the angle to radians:
ϴ = 4 cm / 120 cm = 1/30 rad.
To convert radians to degrees, we use the conversion factor that 1 radian equals 57.2958 degrees.

Therefore, the angle ϴ in degrees is computed as:
ϴ (in degrees) = (1/30) * 57.2958 = 1.91° (correct to two decimal places).