6.3 The Tangent Ratio
B
Hypotenuse
Opposite
C
A
Adjacent
The tangent ratio for acute angle A, is the ratio of the length of the
opposite side (to angle A) over the length adjacent side (to angle A).
opposite
__________
tan A = adjacent
Note: The value of the tangent ratio for a given angle
depends only on the measure of the angle and
not on the size of the right triangle.
1
2
Example 1
Use the tangent ratio to calculate the length of t.
R
t
S
s
40o
r =8 m
T
3
Example 2
Use the tangent ratio to calculate the
measure of B.
B
a
C
c = 10 cm
b = 8 m
A
4
Example 3
Application
In a right triangle, the side adjacent to an angle of 23o is 12 cm long. How long is the side opposite the 23o angle, to the nearest tenth of a centimetre?
5
6
7
8