Honors Geometry_8.5_Feb 7-8
Warm−up
Solve for x,y, and z.
Leave in simplified radical form.
8
45o
x
z
y
8.5
The Tangent Ratio
30o
I can use the Tangent Function to find missing side lengths
and angles of a given right triangle.
I can interpret a real life situation involving right triangles
and the tangent function. [G.SRT.6]
Trigonometry - the study of triangle measurement.
EX 1 Find tan A and tan B.
In a right triangle, the ratio of the lengths of the legs is called the
tangent ratio.
tangent of ∠A =
tan B = ______
leg opposite to ∠A
leg adjacent to ∠A
in abbreviated form:
tan A =
tan A = ______
EX 2 Find tan A and tan B.
A
opposite
tan A = ______
adjacent
10
Note: the value of the tangent of an angle depends only on the size of
the angle not the size of the right triangle.
It represents a RATIO between the opposite side and the adjacent side.
tan B = ______
B
6
C
1
Honors Geometry_8.5_Feb 7-8
EX 3
Use your calculator to find:
(tangent ratios are usually rounded to 4 decimal places.)
Find the value of x to the nearest tenth.
a)
b)
a) tan 33˚ = 0.6494
b) tan 45˚ = 1
c) tan 87˚ = 19.0811
What if I want to find the m∠A?
C
2
B
7
Real life application:
The grade of a road is the ratio of its rise to its run and is usually given
as a decimal or percent.
A
EX 4
Find y correct to the nearest degree.
Warm−up
Find the angle the road makes with the
horizontal if the grade of the road is 7%.
6.1
y˚
4
y=
y=
2
Honors Geometry_8.5_Feb 7-8
More Practice
Find the value of x to the nearest tenth.
1.
24ο
3.
2.
20
x
30
8
5
31
ο
x˚
x
4. A road climbs at an 8˚angle with the horizontal. What is the grade
of the road?
8.5 Assignment:
p. 308 #'s WE 1-19odd, 20-22, 28
3
Honors Geometry_8.5_Feb 7-8
z=54
4