Lesson # 35Trigonometric Ratios

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.

Eg. 2 – To remember the trig ratio formulas think SOHCAHTOA

sin opphyp

cos adjhyp

tan oppadj

theta is used to represent the angle in degrees

Eg. 3 – Calculate to 3 decimal places

a) sin 27o =

b) cos 56o =

c) tan 78o =

d) sin 90o =

e) tan 20o =

f) sin 62o =

0.454 0.559 4.705

1.000 0.364 0.883

What cos60o tells us is that if the angle is 60 degrees theratio of the length of the adjacent over the hyp is 0.5.

60o

1

32opp

adj

hyp

60o

4

488opphyp

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

30o 72.5o

83o

90o 23.3o

45.2o

Eg. 5 Determine unknown measure

Homework

Pg. 228 #2,3,4ab,6-8