1 / 6

Law of Cosines

Law of Cosines. Use to find third side of a triangle Or to solve for unknown angles When c is the hypotenuse of a right triangle we get Pythagoras’ theorem!. c 2 = a 2 + b 2 – 2 ab cos ( θ ). Finding a third side length. When you have 2 lengths and the angle between them.

sawyer
Download Presentation

Law of Cosines

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Law of Cosines • Use to find third side of a triangle • Or to solve for unknown angles • When c is the hypotenuse of a right triangle we get Pythagoras’ theorem! c2 = a2 + b2 – 2abcos(θ)

  2. Finding a third side length • When you have 2 lengths and the angle between them. c2 = a2 + b2 – 2abcosθ = 49 + 144 – 168cos(40°) a = 7 = 64.305 c = 8.02 θ = 40° b = 12

  3. θ = cos-1( ) a2 + b2 – c2 2ab Solving for an angle • When you have all three side lengths c2 = a2 + b2 – 2abcosθ 2abcosθ = a2 + b2 – c2 a = 9 c = 11 θ = 51.75° θ = ? θ = cos-1(0.619) b = 14

  4. Law of Sines ab c • Use to find side length(s) of a triangle • Or to solve for any unknown angle(s) • In a right triangle we get sin(θ) = = = sin(A) sin(B) sin(C) opp hyp

  5. ab sin(A) sin(B) sin(B) = sin(A) b = a· sin(110) sin(40) b = 7· Finding an unknown side length • When you have at least one length and two angles. B = 110° a = 7 b = 10.23 A = 40° b = 10.23 b = ?

  6. Problems • Use the law of cosines to find the measure of the largest angle in a 4-5-6 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.

More Related