Chapter 7

Vocabulary

100

Represented by length of the vector

What is Magnitude

200

The Vector Sum

What is Resultant

300

Each of the Vectors being added

What is component

400

Quantities involving magnitudes

What is Scalars

500

Second Letter of vector name, ending point of vector

What is Terminal Point

Equations

100

The Law of Sins

What is sinA/a = sinB/b = sinC/c

What is a/sinA = b/sinB = c/sinC

200

The Area Formula (that applies to this unit)

What is (1/2)bcsinA; (1/2)absinc; (1/2)sinc

300

b = √[(ccosB-a)² + (c sinB)²]

What is Distance Formula

400

a² = b² + c² - 2bccosA

b² = a² + c² - 2accosB

c² = a² + b² - 2abcosC

What is Law of cosines

500

The Formula of the magnitude of a vector u=<a,b>

What is |u|= √(a² + b²)

Area

100

The area of triangle ABC given C=72.2^o, b=43.8ft, a=35.1ft

What is 732ft²

200

The area of triangle ABC given A=34.97^o, b=35.29m, c=28.67 m

What is 289.9m²

300

The area of triangle ABC given a=22 in., b=45 in., c=31 in.

What is 310in²

400

The area of triangle ABC.  a=25.4 yd, b=38.2 yd, c=19.8 yd

What is approximately 228 yards²

500

The area of the triangle that is formed when figuring out the following problem: A pilot is flying at 168 mph.  The pilot wants the flight path to be on a bearing of 57^o40'.  A wind is blowing form the south at 27.1 mph.  Find the bearing the pilot should sly, and find the plane's groundspeed.

What is 2276.4 units²

Vectors and Magnitudes

100

The solution of u-v, where u=⟨-2, 5⟩ and v=⟨4,3⟩

what is ⟨-6, 2⟩

200

The magnitudes of the horizontal and vertical components of v, if α is the angle of inclination of v from the horizontal, when α= 20^o, |v|= 50

What is |x|= 47 and |y|= 17

300

given u= ⟨-2,5⟩ and v= ⟨4,3⟩

What is ⟨22,9⟩

400

The measure of the direction angle as an angle in [0^o,360^o] where ⟨-4,4√3⟩.

What is θ=120^o

500

The x- and y-components of v, given θ= 75^o, |v|= 100

What is ⟨25.882, 96.593⟩

Find the Side

100

The side length of a, given triangle ABC; C=74.08^o, B=69.38^o, c=45.38m

What is 28.10m

200

The side length of b and c, given triangle ABC; B=38^o40' a=19.7cm, C=91^o40'

What is 16.1cm and 25.8cm

300

The side length of b₁ and b₂, given triangle ABC; C=29^o50', a=8.61m, c=5.21m

What is 10.4m and 4.51m

400

The side length of a, given triangle ABC; A=41.4^o, b=2.78yd, c=3.92yd

What is 2.60yards

500

The side length of c, given triangle ABC; b=60, a=82, B=100^o 

What is No Solution.  Triangle does not exist.