# Ch 7  Applications of Trigonometry and Vectors

## Ch 7.1  Oblique Triangles and the Law of Sines :

The Law of Sines: The Basics :
Solving the Triangle with A=48°, B=54°, a=12.5ft

Solving the Triangle with C=102°, b=5m, c=18m

Finding the Distance Across the Canyon

Finding the Distance of the Campsite from the Base of the Mountain and the Time Needed to the Base

Determining the Length of X

Determining the Distance from the Tower to the Airplane
Determining the Elevation of the Airplane

Determining the Area of a Triangle with A=35°, a=6cm, a=15cm
Determining the Area of a Triangle with B=72°, a=23.7 ft, b=25.2 ft

## Ch 7.2  The Ambiguous Case of the Law of Sines

Solving the Triangle with C=82°, a=11m, c=7m;
Solving the Triangle with A=88°, a=110ft, c=54ft;
Solving the Triangle with B=40°, b=22cm, a=30cm

Solving SSA (Side, Side, Angle) Triangle (Ambiguous Case) with One solution given a=76, c=52, A=39° http://www.youtube.com/watch?v=CXU-zGTfHGM&feature=plcp

Solving SSA (Side, Side, Angle) Triangle (Ambiguous Case) with Two solutions given a=52, b=63, A=42°  http://www.youtube.com/watch?v=sXn_rkJE3WI&feature=plcp

Solving SSA (Side, Side, Angle) Triangle (Ambiguous Case) with No solutions given a=48, c=68, A=86° http://www.youtube.com/watch?v=u8zLE0buKPY&eature=plcp

## Ch 7.3  The Law of Cosines

Solving Triangle ABC with B= 73.1°, a= 24.2 ft, c= 43.7 ft
Solving Triangle ABC with a= 25.4cm, a=42.8cm, c=59.3cm

Determining the Diagonal of a Parallelogram

Determining the Length of the Tunnel and the Bid Amount after 20% profit off the Cost
Determining the Duration of Service a Person gets when She is Driving Past a Transmission Tower at a Certain Speed

Determining the Flying Distance of A plane From Her Starting Position

The Law of Cosines: Applications – Determining the Largest Angle of the Three Sides

Determining the Areas of Triangles Using Heron’s Area Formula

## Ch 7.4  Vectors, Operations, and the Dot Product

Introduction to Vectors :

Vector Basics – Drawing Vectors/ Vector Addition

Finding x and y Components of a Vector with a Magnitude of 8 and at an Angle of 60° from the Origin

Finding x and y Components of Vectors

Drawing the Vector v=<2,3>;
Drawing the Vector   v=<–3,4>;
Finding the Vector  AB of (2, 1) and (5, 6)

Adding v+u and v+u+w  where v=<2, 2>, u=<3, 0> and w=<0, –6>;
Multiplying 10u  where u=<1, 4>;
Simplifying u–2w  where  u=<1,4> and w=<–2, 3>

Finding the Magnitude and Direction of Vector <–3, 4>

Finding the Magnitude and Direction of Vector <–2, –5>

Finding the Magnitude and Direction of Vector <2, 6> and <3, –10>

Finding Dot Products a·b  where a=<2, 5> and b=<–3, 1>;
Finding the Angle of a=6i–2j–3k and b=i+j+k;
Determining if a=<2, 4> and b=<4, –2> are Orthogonal

Finding Dot Product u·v  and u(v+w) Givern v=<-1, 5> andw=<–3, 1>;
Angle Between Two Vectors;

Parallel and Orthogonal Vectors;

Finding the Angle Between u=<-2, 3> and v=<1, -5>;
Determining if Two Vectors u=<-4, 2> and v=<1, 2> are Orthogonal;

Definition of the Component of Vector a along Vector b; http://www.youtube.com/watch?v=c5mSscgulIXg&list=PL554F9F460401DF50&index=38&feature=plpp_video

## Ch 7.5  Applications of Vectors

Finding the Distance between the Ship and the Port and its Bearing
Finding the Direction and Magnitude of the Resultant Force of Two Trucking Pulling on a Truck Stuck in the Mud