Hour: 134 Date: 3 10130
Geometry - Law of Sines and Cosines Quiz Review
c = a + b2 - 2abcos C C=cos- c-aʻ- b' sin A sin B sin
-2ab a b c
Use the Law of Cosines to solve problems #1 & 2. You must show all work for credit.
1. Find side AB
5
78°
Hour: 134 Date: 3 10130
Geometry - Law of Sines and Cosines Quiz Review
c = a + b2 - 2abcos C C=cos- c-aʻ- b' sin A sin B sin
-2ab a b c
Use the Law of Cosines to solve problems #1 & 2. You must show all work for credit.
1. Find side AB
5
78°
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.
[tex][/tex]
[tex]Atrain goes up a hill with a 15º incline. if the train has constant speed of 22 m/s, what are the ve[/tex]
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.
Any two-dimensional vector in cartesian (x,y) coordinates can be broken down into individual horizontal and vertical components using trigonometry. If a train goes up a hill with 15 degree incline at a speed of 22 m/s, the horizontal component is 22cos(15)=21.3 m/s and the vertical component is 22sin(15)=5.5 m/s.
X= 9.46
Hope this help you