8-5B The Law of Cosines Geometry

Law of Cosines You can solve SAS and SSS given using the Law of Cosines:

Ex. 1 Find XZ. Round lengths to the nearest tenth and angle measures to the nearest degree. Y 35 110° 30 X Z

Ex. 2 Find m∠T. Round lengths to the nearest tenth and angle measures to the nearest degree. T 11 R 13 7 S

Ex. 3 A sailing club has planned a triangular racecourse, as shown in the diagram. How long is the leg of the race along BC? How many degrees must competitors turn at point C? Round the length to the nearest tenth and the angle measure to the nearest degree. C 3.1 45° A 3.9 B

Ex. 4 The lengths of the sides of a triangular plot of land are 120 feet, 150 feet & 175 feet. Find the largest angle of the triangle.

Assignment

Heron’s Formula (Greek mathematician AD 100)

Ex. 4 Find the area of C a=12 b=14 B c=17 A

Law of Cosines You can solve SAS and SSS given using the Law of Cosines:

Ex. 5 The triangular region shown is a child’s block. Find the volume of the block.