Atrain goes up a hill with a 15º incline. if the train has constant speed of 22 m/s, what are the vertical and horizontal components of the train's velocity? (remember to use the law of sine and cosines for this problem)

Sinθ=opposite side/hypotenuse
cosθ=adjacent side/hypotenuse
where both the sides are relative to theta.

in this case, 22 is your hypotenuse. theta (θ) is the angle you are examining. i've included a diagram for reference because the equations may format differently depending on which angle you choose as theta. 

using my diagram:

sinθ = o/h
sin 15 = o/22
sin 15(22) = o
o=5.69m/s

therefore the vertical component is about 5.69m/s.

cosθ=a/h
cos15 = a/22
cos15(22) = a
a = 21.25m/s

therefore, your horizontal component is about 21.25m/s.

32

step-by-step explanation:

these are your clues: 1. kim ran 18 races2. this was four fewer races than twice thenumber, notice it says twice the number, so you would do the equation 18x2-4; which equals the number 32.thus, 32 is your answer.