The hour hand on a clock is 4 cm long, and the minute hand is 10 cm long. What is the exact distance between the tips of the hands at 10 o'clock?

2 sqrt (19)

Step-by-step explanation:

We know that the angle between the two hands

360 / 12 * 2 = 60 degrees

We divide by 12 because there are 12 number and multiply by 2 because there are 2 number between 10 and 12

This is a triangle where we know 2 sides and the angle between them.

We can use the law of cosines to determine the third side

c^2 = a^2 + b^2 - 2abcosC

Where C is the angle between sides a and b

a = 4 and b = 10 C = 60 and we are looking for side c

c^2 = 4^2 + 10^2 - 2*4*10 cos60

c^2 = 16+100 - 80cos 60

c^2 = 76

Take the square root of each side

sqrt (c^2) = sqrt (76)

c = sqrt (76)

c = sqrt (4) sqrt (19)

c = 2 sqrt (19)