Interactive Demonstration of the Law of Cosines Formula
The interactive demonstration below illustrates the Law of cosines formula in action. Drag around the points in the triangle to observe who the formula works.
The two common problems types that are suitable for the law of cosines are.
Problem type 1: when you know the lengths of 2 sides of a triangle and the angle in between the two sides
Problem type 2: when you know the lengths of three sides of a triangle and want to know a particular angle
Practice Problem 3)
Use the law of cosines to calculate x.
Step 1: set up formula
25² = 32² + 37² −2(32)(37)cos(x)
Solve the equation
625 = 2393 − 2,368 cos(x)
Practice Problem 4)Use the law of cosines to calculate the measure of the shaded anlge.
Step 1: set up formula
14² = 20 ² + 12² −2(12)(20)cos(angle)
Solve the equation
Solve the equation in terms of cos(angle) and then use cos-1 to determine the angle measurement
The law of Cosines and the pythagorean theorem.
Use the law of cosines to calculate the value of x. This exercise should help you see the connection between the law of cosines and the pythagorean theorem.
sohcahtoa worksheet
Use the law of cosines to calculate x.
Use the law of cosines to calculate the measure of the shaded anlge.
1)
Use the law of cosines formula to calculate the length of side A.