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Make sure the calculator is in Degree Mode (DRG button) Practice getting the sine/cos/tan of various angles Inverse functions: [2nd F button] Use of backets is important when finding inverses: e.g 3 5 -1 3 A Sin 5 If Sin A 2 SECTION 1 RIGHT ANGLED TRIANGLES RIGHT ANGLED TRIANGLES A A ADJACENT ADJACENT 900 900 PYTHAGORAS THEOREM c a b a2 +b2 = c2 The square of the hypotenuse is equal to the sum of the squares on the other 2 sides. This theorem is used when you are looking for the length of one side of a triangle when you are given the measurements of the other 2 sides. ( Remember this theorem only works for right angled triangles). Hypotenuse [H] Hypotenuse [H] Opposite [O] A Adjacent [A] A Hypotenuse [H] Adjacent [A] Opposite [O] Cosine Cos A = A H [O] Sine Sin A = [H] O H A Tangent Tan A = [A] O A SOHCAHTOA [5] [H] [O] [3] A [4] SOHCAHTOA [A] Sin A = O H = 3 5 [5] [H] [O] [3] A [4] SOHCAHTOA [A] Cos A = A H = 4 5 [5] [H] [O] [3] A [4] SOHCAHTOA [A] Tan A = O A = 3 4 [13] [H] [O] [12] A [5] SOHCAHTOA [A] Sin A = O H = 12 13 [13] [H] [O] [12] A [5] SOHCAHTOA [A] Cos A = A H = 5 13 [13] [H] [O] [12] A [5] SOHCAHTOA [A] Tan A = O A = 12 5 [O] x [15] Looking for x O Given H [H] Sin 300 O = = H Sin 300 = 0.5 300 [A] SOHCAHTOA x 15 x = 0.5 1 = 15(0.5) = 7.5 x 15 Looking for x O Given A [H] [O] x tan 50o O = A = x 15 Tan 50o = 1.1917 500 [15] [A] SOHCAHTOA x 15 x = 1.1917 1 = 15(1.1918) = 17.876 x [O] [H] Looking for x H Given A Cos 35o A 16’ = H = 15 x Cos 35o 16’ = 0.8164 15 35o 16’ [15] [A] SOHCAHTOA x = x(0.8165) x= 0.8164 1 = 15 15 0.8165 = 18.37 THE ANGLE OF ELEVATION AND DEPRESSION (a) Angle of depression = Angle looking down (b) Angle of elevation = Angle looking up depression elevation QUESTIONS ON RIGHT ANGLED TRIANGLES Example 1 A plane takes of at an angle of 200 to the level ground. After flying for 100m how high is it off the ground. 100m 200 900 100m 900 200 In this we are given the Hyp. And we are looking for the Opp So we use the Sin Formula Opp h Sin 20 Hyp 100 h 0 .342 100 Sin20 0.3420 h 34.2m Example 2. A building 14m heigh casts a shadow 10m in length Find the angle of elevation of the sun. 14m x 10m Opp Tan x Adj 14 Tan x 1.4 10 x 5428' Example 3. A ladder 10m long just reaches the top of a wall 8m high. Find the angle between the ladder and the wall. 8m 10m Adj Cos Hyp Cos 8 .8 10 36 53' 5 Example 4. If Cos , find Sin and Tan 2 , 0 90 13 without using calculator. Note: If given ratio always draw right angled triangle x Adj = 5 Adj 5 Cos Hyp 13 By Pythagoras 13 2 x 2 5 2 x 12 (Note triplet) Opp 12 Sin Hyp 13 2 144 Opp 12 2 2 Tan (Tan ) 25 Adj 5 2