5.6 Law of Cosines
What you’ll learn about Deriving the Law of Cosines Solving Triangles (SAS, SSS) Triangle Area and Heron’s Formula Applications … and why The Law of Cosines is an important extension of the Pythagorean theorem, with many applications.
Law of Cosines
Example Solving a Triangle (SAS)
Example Solving a Triangle (SAS)
Example Solving a Triangle (SAS)
Area of a Triangle
Heron’s Formula
Example Using Heron’s Formula Find the area of a triangle with sides 10, 12, 14.
Example Using Heron’s Formula Find the area of a triangle with sides 10, 12, 14.
Quick Review
Quick Review
Quick Review
Chapter Test
Chapter Test
Chapter Test 9. A hot-air balloon is seen over Tucson, Arizona, simultaneously by two observers at points A and B that are 1.75 mi apart on level ground and in line with the balloon. The angles of elevation are as shown here. How high above ground is the balloon?
Chapter Test 10. A wheel of cheese in the shape of a right circular cylinder is 18 cm in diameter and 5 cm thick. If a wedge of cheese with a central angle of 15º is cut from the wheel, find the volume of the cheese wedge.
Chapter Test Solutions
Chapter Test Solutions
Chapter Test Solutions 9. A hot-air balloon is seen over Tucson, Arizona, simultaneously by two observers at points A and B that are 1.75 mi apart on level ground and in line with the balloon. The angles of elevation are as shown here. How high above ground is the balloon? ≈ 0.6 mi
Chapter Test Solutions 10. A wheel of cheese in the shape of a right circular cylinder is 18 cm in diameter and 5 cm thick. If a wedge of cheese with a central angle of 15º is cut from the wheel, find the volume of the cheese wedge. 405π/24 ≈ 53.01