Question

A circular clock face, centre O, has a minute hand OA and an hour hand OB. OA= 10 cm. OB = 7 cm. Calculate the length of AB when the hands show 5 o'clock. Give your answer correct to 3 significant figures. 10 cm 0 7 cm B Diagram NOT accurately drawn​

Answer 1

The length of arc AB is 26.2 cm.

From the information given, we have;

The central angle between OA and OB when the hands show 5 o'clock can be determined by;

`30^(o)` * 5 =
`150^(o)`

length of an arc = (θ/ 360)*2
`\pi`r

where r is the radius of the circle, and θ is the central angle.

length of arc AB =
`(150)/(360)` * 2* 3.14 * 10

= 0.4167* 62.8

= 26.17

length of arc AB = 26.17 cm

The length of AB when the hands show 5 o'clock is 26.2 cm.