A CHORD 9CM LONG SUBTEND AN ANGLE OF 30DEGREE AT THE CENTRE OF THE CIRCLE,CALCULATE THE RADIUS OF THE CIRCLE.
Draw the diagram. It should be clear that
4.5/r = sin 15°
r = 17.39
The answer is 17.4cm
To calculate the radius of the circle, we can use the formula relating the length of the chord, the angle it subtends, and the radius of the circle. The formula is:
r = (c / 2sinθ)
Where:
- r is the radius of the circle
- c is the length of the chord
- θ is the angle subtended by the chord at the center of the circle
In this case, the length of the chord is 9 cm, and the angle subtended by the chord at the center of the circle is 30 degrees.
Substituting these values into the formula:
r = (9 / 2sin30)
To evaluate sin30, we need to know the value of sin30 degrees. So let's calculate it:
sin30 degrees = 0.5
Now let's substitute this value back into the formula:
r = (9 / 2 * 0.5)
= 9 / 1
= 9 cm
Therefore, the radius of the circle is 9 cm.