Name: _______________________________________ Date: __________ Lesson 2.26 – Law of Cosines CC Geometry Do Now: Coastguard station A is 12 miles west of coastguard station B along a straight coastline. A ship is sited by the crew at station A to the northeast of the station at an angle of 35 degrees with the coastline and by the crew at station B to the northwest of the station at an angle of 46 degrees with the coastline. Find, to the nearest tenth, the distance from the ship to each of the stations.

Examples: 1. In

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'ABC , side b = 12, side c = 20 and

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m�A = 40

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o. Find the length of side a to the nearest integer.

Law of Cosines

c2 = a2 + b2 – 2 a b cosC

b2 = a2 + c2 – 2 a c cosB

a2 = b2 + c2 – 2 b c cosA

Answer key 2/3

2. A triangular walking course has 2 sides of 230 feet and 360 feet, and the angle between these sides measures

38º. Find the length of the third side of the course, to the nearest foot.

3. Find the value of x, to the nearest tenth, in each.

a. b. c. d.

Mixed Practice with Law of Sines and Law of Cosines: Find the value of x, to the nearest integer, in each.

1. 2. 3. 4. 5. 6.