The Law of Sines is very applicable in the real world. The Law of Sines helps to measure things like lakes, ravines, or other objects that are hard to measure directly. The Law of Sines can be used to solve for any part of a triangle that is unknown when we are given two angles and an included side (ASA), two angles and a non-included side (AAS), or the ambiguous case two sides and a non-included angle (SSA). The ambiguous case can yield no solutions, one solution, or two solutions. When given side-side-angle, be very careful in recognizing that there are three possibilities for the triangle.
The Law of Cosines is also very applicable in the real world. The Law of Cosines helps to measure things like lakes, ravines, or other objects that are hard to measure directly. The Law of Cosines can be used to solve for any part of a triangle that is unknown when we are given two sides and an included angle (SAS) or all three sides (SSS). After using Law of Cosines to find the first missing measurement, we can use Law of Sines to find the rest. It is always best practice, if given all three sides to find the angle measure across from the largest side first. After finding this value, when using Law of Sines, use the smallest side or angle to find the next missing value. This ensures that you won't end up with the ambiguous case of two different values that work, which can confuse the situation.
Law of Cosines Given Side Angle Side (SAS)
Law of Cosines Given all Three Sides (SSS)
Finding Area of Triangles
Traditionally, we find the area of a triangle by doing one half the base times the height. This is great if you have a right triangle, or are given the base and the height. In this section, we will find area of an oblique triangle (a triangle that is not right) and the area of a triangle when given all three sides. There can be times in the real world where we have to find the area of the triangles by using alternative area formulas.
Vectors are quantities with both magnitude and direction. Vectors are useful in Physics as well as Mathematics. Vectors utilize the coordinate plane, and the endpoints act like an ordered pair. The videos in this section will cover various topics of vectors as well as applications.
Find Magnitude and Direction Angle of a Vector
Horizontal and Vertical Components of a Vector
Operations on Vectors
Find Resultant Force of Two Vectors
Dot Product
Angle Between Vectors
Orthogonal Vectors
Application - Find Distance Boat is from Starting Point
Application - Find Speed of Current and Speed of Boat