Law of Cosines

We use law of Cosines to find the length of a missing side or degree of a missing angle in an Oblique triangle(No Right Angle)

In order to do this we must have some information and there are 4 conditions that will work, however only 2 use the law of Cosines, so we will focus on those today.

In order to use law of Cosines you must know:

1.) all 3 sides SSS2.) 2 sides and the included angle SAS

A

BCa

b cThe three angles are A, B, and C with the side opposite the angles being a, b, and c.

Law of CosinesLaw of Cosines: when you know 3 sides. Law of Cosines: When you know 2

sides and the included angle.

a2 = b2 + c2 – 2bcCosA

b2 = a2 + c2 – 2acCosB

c2 = b2 + a2 – 2baCosC

These are the same equations they have just been solved for different parts.

A golfer hits an errant tee shot that lands in the rough. A marker in the center of the fairway is 150 yards from the center of the green. While standing on the marker and facing the green, the golfer turns 1100 toward his ball. He then paces 35 yards to his ball. How far is the ball from the green?

35 yds

150 yds

1100

x

You Try

In attempting to fly from Chicago to Louisville, a distance of 330 miles, a pilot inadvertently took a course that was 100 in error, as indicated in the figure.(a) If the aircraft maintains an average speed of 220 miles per hour and if

the error in direction is discovered after 15 minutes, through what angle should the pilot turn to head toward Louisville?

(b) What new average speed should the pilot maintain so that the total time of the trip is 90 minutes?

330 mi

100

louisville

Assignment #1 Pg. 535 (43-49 odd)