6.5 Law of Cosines

Law of Cosines – use if know 2 sides and the included angle or all 3 sides The square of any side of a triangle is equal to the sum of the squares of the other 2 sides minus twice the product of those two sides times the cosine of the included angle. If one of the angles of a triangle is a right triangle then cos C = 0 and the Law of Cosines becomes ___________________.

A B C 65º 5 8 Ex – Solve the triangle

EX – solve the triangle The sides of a triangle are a = 76.536, b = 39.701, and c = 63.14. Find the angles. A B C 63.14 76.536 39.701

Ex – solve the triangle Angle A = 46.3º, b = 8.6 and c = 14.4. 8.6 C A 46.3° 8.6

Heading & Bearing In navigation a direction is often given as a bearing.

Ex – pg 515 #41 A pilot flies in a straight path for 1 hour and 30 minutes. She then makes a course correction, heading 10º to the right of her original course and flies 2 hours in the new direction. If she maintains a constant speed of 625 mph, how far is she from her starting position?

Heron’s formula The area of a triangle ABC is given by: Where

Pg 513 ex5 A businessman wishes to buy a triangular lot downtown. The lot’s three sides are 125, 280, and 315 ft. Find the area of the lot.

pg 513 #1-25 odd, 37-39 all Homework