1. World 5-1 Trigonometric Ratios

2. Recall that in the past finding an unknown side of a right triangle required the use of Pythagoras theorem. By using trig ratios we can now solve unknown sides of a triangle and determine all the angles. No more Pythag! Eg.1- First we must label the sides properly Adjacent Opposite Hypotenuse Opposite Adjacent Hypotenuse The adjacent side always touches the angle.

3. Eg. 2 – To remember the trig ratio formulas think SOHCAHTOA sin  opp hyp cos  adj hyp tan  opp adj  theta is used to represent the angle in degrees Eg. 3 – Calculate to 3 decimal places a) sin 27 o = b) cos 56 o = c) tan 78 o = d) sin 90 o = e) tan 20 o = f) sin 62 o = 0.454 0.559 4.705 1.000 0.364 0.883

4. What cos60 o tells us is that if the angle is 60 degrees the ratio of the length of the adjacent over the hyp is 0.5. 60 o 1 3 2 opp adj hyp 60 o 4 48 8 opp hyp adj To determine the unknown angle press sin -1, cos -1, or tan -1 Eg. 4 – Calculate the angle to 1 decimal place a) sin  = 1/2 b) cos  = 0.3 c) tan  = 8.1 d) sin  = 1 e) tan  = 0.43 f) sin  = 0.71 30 o 72.5 o 83 o 90 o 23.3 o 45.2 o

5. Eg. 5 Determine unknown measure d)

6. Homework World 5-1 Handout