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MAP4C
Primary Trigonometric Ratios
Trigonometry – the study of triangle measures (3 side lengths, 3 angles)
Primary Trig. Ratios – relate the sides of a right triangle with respect to one of the acute (less
than 90˚) angles
Recall: SOH CAH TOA
opposite
hypotenuse
adjacent
cos  
hypotenuse
opposite
tan  
adjacent
sin  
Ex1
opposite
hypotenuse

adjacent
List the three primary trig. ratios for the following triangle
opposite
4

hypotenuse 5
adjacent 3
cos  

hypotenuse 5
opposite 4
tan  

adjacent 3
sin  
5m
4m

3m
Ex2
Use your calculators to find: (make sure it is in degree mode)
a) sin 32˚ =
Ex3
b) cos 80˚ =
Find the missing side length:
x
32°
7.1 cm
Steps:
Label the sides of the triangle as opp, adj, hyp
Pick the appropriate ratio based on the values given
Substitute into the formula
Cross-multiply to solve
c) tan 15˚ =
Ex4
Solve the following triangle:
A
24°
B
8.4 cm
C
Find the value of P to the nearest degree:
Ex5
R
Ex6
12 cm
5 cm
P
Q
Solve triangle ABC when  B = 90˚, b = 4.1 m, and c = 3.9 m.
Word Problems
Recall: Angle of elevation – from a horizontal plane looking up
Angle of depression – from a horizontal plane looking down
Ex7
A person at the top of a tower measures the angle of depression to a car on the ground
to be 12˚. If the tower is 200 m high, how far is the car from the base of the tower?
Ex8
The gradient of a hill is 8%. What is the angle of elevation to the top of the hill?