Question

A.Find the measure of the angle swept by the hour hand between noon and 9:55 pm

Answer 1

Answer:

(a) The angle swept by the hour hand is 297⁰30′  

(b) The exact angle between the minute and hour hand is 132⁰30′

Step-by-step explanation:

Given;

(a) angle swept by the hour hand between noon and 9:55 pm

between 12 pm and 9pm, there are 9 hours = 9 x 60 = 540 mins

9.55 pm = 540 mins + 55 mins = 595 mins

The hour hand moves  0.5 degree per minute

1 mins ---------------- 0.5 degrees

595 mins --------- ?

= 297⁰30′  

(b) the exact angle between the minute and hour hands at 1:25 pm

for 25 mins, the hour hand had moved 12.5 degrees

Between 1 and 5, there are 20 mins moved by the minutes hand = 20 x 6°

= 120⁰

total angle = 12.5⁰ + 120⁰ = 132⁰30′