1. 9-1 The Tangent Ratio 4/26/17 T an A = pposite djacent O A
Objective: To use tangent ratios to determine side lengths in right triangles. B B T
an A = pposite
djacent O
Hypotenuse A
Opposite A A C C
Adjacent
What is Soh Cah Toa?
Soh Cah TBD…

2. Reciprocals! T 5 4 V U 3 Ex: Find tan T = opp = UV = 3 adj TV 4
Find tan U = opp = TV = 4
adj UV 3 U
T V
Write tangent ratios for K and J. How is tan K related to tan J? J 3
L K T 5 4 V U 3
Tan K = 3 7
Tan J = 7 3
Reciprocals!

3. Make sure the calc is in DEGREE mode!!!!
Find x
Ex: Use a calculator o
tan 86o = x 50
50(tan 86o) = x
In calc:
50 • tan 86 =
About 715
Find w to the nearest tenth.
1) ) y
54o o w 3) w
57o o x x
Tan 28 = 10 y
Tan 54 = w 10
y •Tan 28 = 10
10 •(Tan 54) = w
y = e
= 18.8
w = 13.8
(Tan 28)
Tan 57 = w
2.5
Tan 33 = 2.5 w
w = 3.8
w = 3.8
It works either way!

4. Ex: Find m x to the nearest degree. tan x = 6 = .75 H 8
Tan-1 (.75) is asking “what angle has a tangent of .75?”
It is called the Inverse Tangent. Tan-1  that is NOT a power!
Ex: Find m x to the nearest degree.
tan x = 6 = H 8
m x = tan-1(0.75)
tan =
m x B X
Find m Y to the nearest degree.
P T 41 Y
m y = Tan-1 (100/41)
= 68°
You might want to do 100/41 first, then calculate the Tan-1 depending on how your calc works.

5. x K 8 L 15 M Write the tangent ratio for K
Write the tangent ratio for M
Find m M to the nearest degree
Find x to the nearest whole number
1) )
40o
x o 15 8
8 15
m M = Tan-1 (8/15)
= Tan-1 (.5333) = 28°
Tan 40 = x 62 x x
Tan 72 = 90 x
x = 52
x = 29

6. (When the circle has a radius of 1, that is.)
Assignment: Page 472 #1 – 20