Question

How long is the minute hand on a clock whose tip travels 15 cm from 1:15 to 1:30 to the nearest tenth?

Answer 1

We can model the trip of the clock hand as shown in the picture below:

The clock hand is of the same length, '$x$' and it forms a right-angle triangle from 1:15 to 1:30

We can use the Pythagoras theorem to find the length of the minute hand

$x^2+x^2=15^2$
$2x^2=225$
$x^2= \frac{225}{2}$
$x^2=112.5$
$x= \sqrt{112.5}$
$x=10.6$ 

Answer : 10.6 (to the nearest tenth)

Answer 2

Answer:

The length of minute hand is 9.5 cm

Step-by-step explanation:

We are given the minute hand move from 1:15 to 1:30

Time for 1:30 to 1:30 = 15 minutes

Tip of minute hand move 15 cm in 15 minutes.

In 60 minutes = 360°

   In  1 minute = 6°

In 15 minutes = 90°

Formula: $\theta=\dfrac{L}{r}$

$\theta=90^\circ$

Now we change $\theta=90^\circ$ into radian

$Radian=\dfrac{\pi}{180^\circ}\times 90^\circ=\dfrac{\pi}{2}$

L=15 cm

R = Length of minute hand.

$\dfrac{\pi}{2}=\dfrac{15}{R}$

$R=\dfrac{30}{\pi}\approx 9.5$

Hence, The length of minute hand is 9.5 cm