Presentation on theme: "Law of Cosines c2 = a2 + b2 – 2abcos(θ) Or to solve for unknown angles"— Presentation transcript:
1Law of Cosines c2 = a2 + b2 – 2abcos(θ) Or to solve for unknown angles Use to find third side of a triangleOr to solve for unknown anglesWhen c is the hypotenuse of a right triangle we get Pythagoras’ theorem!
2Finding a third side length When you have 2 lengths and the angle between them.c2 = a2 + b2 – 2abcosθ= – 168cos(40°)a = 7=c = 8.02θ = 40°b = 12
3Solving for an angle When you have all three side lengths c2 = a2 + b2 – 2abcosθ2abcosθ = a2 + b2 – c2a = 9c = 11θ = cos-1 ( )a2 + b2 – c22abθ = 51.75°θ = ?θ = cos-1(0.619)b = 14
4Law of Sines a b c = = sin(A) sin(B) sin(C) Use to find side length(s) of a triangleOr to solve for any unknown angle(s)In a right triangle we get sin(θ) =opphyp
5Finding an unknown side length When you have at least one length and two angles.sin(A) sin(B)a b=sin(A)sin(B)b = a·sin(40)sin(110)b = 7·B = 110°a = 7b = 10.23A = 40°b = ?b = 10.23
6ProblemsUse the law of cosines to find the measure of the largest angle in a triangle.Use the law of sines to find the shortest side in a 40°-60°-80° triangle whose longest side is 10.0 cm.A triangle has known angles of 37° and 55°. The side between them is 13 cm long. Find the other side lengths.A plane which is 100 miles due West of you moves in a roughly Northerly direction at 400 mph. If after 10 minutes the new distance to the plane is 130 miles, determine the exact heading of the aircraft.