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)

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above