8­3 Tangent Ratio 2011 February 07, 2011
8­3 Tangent Ratio
Objective- use the tangent ratio
to determine side lengths and
angles in right triangles.
Jan 30­9:10 PM
1
8­3 Tangent Ratio 2011 February 07, 2011
For numbers 1-3 identify the length of:
a. the hypotenuse
b. the side opposite angle B
c. the side adjacent to angle B.
4. Sketch a 30-60-90 triangle and label the sides.
Use "s" as your short side
Jan 30­9:15 PM
2
8­3 Tangent Ratio 2011 February 07, 2011
RECAP
Equations to find sides in 45-45-90 triangles
45
l√2
l
90
45
l
30
Equations to find sides in 30-60-90 triangles
2s
s√3
90
60
s
Jan 31­11:38 AM
3
8­3 Tangent Ratio 2011 February 07, 2011
So what the heck is the tangent ratio?
Lets find out.
Jan 30­9:23 PM
4
8­3 Tangent Ratio 2011 February 07, 2011
Measurements
Feb 2­10:25 AM
5
8­3 Tangent Ratio 2011 February 07, 2011
So the tangent ratio is...
Important!
As long as the angles are the same,
this ratio is the same no matter
what size the triangle is!
Jan 30­9:25 PM
6
8­3 Tangent Ratio 2011 February 07, 2011
Lets try it. Quietly. On our own.
Find the length of w.
tan(A)
Opposite
Adjacent
Feb 2­10:53 AM
7
8­3 Tangent Ratio 2011 February 07, 2011
Where else would we use this stuff besides class???
Used to find distances that are
impossible to directly measure.
Jan 31­12:24 PM
8
8­3 Tangent Ratio 2011 February 07, 2011
Find the distance, x, from the earth
to the moon using the tangent ratio.
3,950 mi
o
0.955
x
Jan 31­2:04 PM
9
8­3 Tangent Ratio 2011 February 07, 2011
We found side lengths,
how do we find angles?
Consider:
5A=10
Using Inverses!
tan-1
tan(A)
20
Feb 2­10:59 AM
10
8­3 Tangent Ratio 2011 February 07, 2011
Again. Lets try it. Quietly. On our own.
Find m X.
tan(X)
Opposite
Adjacent
Feb 2­11:09 AM
11
8­3 Tangent Ratio 2011 February 07, 2011
Homework
Pg. 434 # 1 - 9 odd,
11 - 15 odd, 22, 24, 31
Feb 2­11:12 AM
12