1. Unit 3: Right Trigonometric Ratios

2. Use these calculator keys
When do I use…?
I want to find
Use these calculator keys
sin, cos or tan
(ratio)
SIN
COS
TAN
Angle measure
(in degrees)
SIN-1
COS-1
TAN-1

3. The three trigonometric ratiosθ O P S I T E H Y N U
A D J A C E N T
Opposite
S O H
Sin θ =
Hypotenuse
Adjacent
C A H
Cos θ =
Hypotenuse
You must learn these three trigonometric ratios.
Remember these using SOHCAHTOA or make up your own mnemonics using these letters.
Opposite
T O A
Tan θ =
Adjacent

4. Finding side lengths
If we are given one side and one acute angle in a right-angled triangle, we can use one of the three trigonometric ratios to find the lengths of other sides.
Find x to 2 decimal places.
To find the length of the side opposite the angle, given the hypotenuse, use:
56° x
12 cm
opposite
sin θ =
Remember to use the trigonometric ratio based on the information that you have.
Draw a picture if necessary.
hypotenuse x
sin 56° = 12
x = 12 × sin 56°
= 9.95 cm

5. Finding side lengths
A 5 m ladder is resting against a wall. It makes an angle of 70° with the ground.
What is the distance between the base of the ladder and the wall?
To find the length of the side adjacent to the angle, given the hypotenuse, use:
5 m
adjacent
cos θ =
hypotenuse x
70°
cos 70° = x 5
x = 5 × cos 70°
= 1.71 m (to 2 d.p.)