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°

Skip to content# Hour: 134 Date: 3 10130Geometry – Law of Sines and Cosines Quiz Reviewc = a + b2 – 2abcos C C=cos- c-aʻ- b’ sin A sin B sin-2ab

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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